
122 Ill. App.3d 141 (1984)
460 N.E.2d 858
THE PEOPLE OF THE STATE OF ILLINOIS, Plaintiff-Appellee,
v.
JOHNNY DIXON, Defendant-Appellant.
No. 81-700.
Illinois Appellate Court  First District (5th Division).
Opinion filed February 24, 1984.
*142 *143 George P. Lynch, of Chicago, for appellant.
*144 Richard M. Daley, State's Attorney, of Chicago (Michael E. Shabat, Lawrence R. Stasica, and Timothy J. Joyce, Assistant State's Attorneys, of counsel), for the People.
Judgment affirmed and cause remanded.
PRESIDING JUSTICE MEJDA delivered the opinion of the court:
Defendant Johnny Dixon appeals from his conviction, following a bench trial, for the offenses of murder, burglary and home invasion. Sentence was imposed only for murder. He raises four issues on appeal: (1) whether the court erred in failing to obtain a waiver of jury for the sentencing hearing; (2) whether defendant was improperly convicted for the offenses of burglary and home invasion; (3) whether defendant was illegally sentenced; and (4) whether defendant was proved guilty beyond a reasonable doubt of the offenses of murder, burglary and home invasion. We affirm and remand for sentencing as to burglary and home invasion.
The following testimony was presented at trial.
Robert Thomas testified that on February 4, 1979, he was in the living room of a residence located at 5532 South La Salle Street with his niece, Lauretta Hullett, Sandra Thomas, and the owner of the property, Joan Hullett. About 10 p.m. there was a knock at the front door. He and Lauretta looked through the window in the door and saw a man standing on the porch. The porch was illuminated by two nearby streetlights and by light from inside the house. Neither he nor Lauretta recognized the man. The man wore wire frame glasses, a dark blue knit cap and a pea coat and carried a police radio. He announced that he was from the "State's Attorney's police" and displayed a black wallet containing a star-shaped badge and identification card. Robert viewed the man for about 30 seconds, then with Joan Hullett's permission, opened the door. The man on the porch raised a handgun, placed one foot inside the door and fired the gun. Robert succeeded in closing the door after a brief struggle. Lauretta was taken to the hospital and pronounced dead. Robert identified the defendant in court as the man who had been on the porch.
Robert further testified that on February 10, 1979, he viewed photographs at the police station. In court he selected a photograph of the defendant and stated that it was the same photograph he had chosen on February 10 as depicting the man who shot Lauretta. On November 27, 1979, Thomas viewed a lineup and identified the defendant as the man who shot Lauretta.
Robert stated that the radio carried by the man was a hand-held scanner type with a flexible antenna. Before opening the front door *145 he heard transmissions emitting from the radio of the same type as would be heard from a police scanner. The glasses worn by the man on the porch had grayish frames. In court Thomas identified glasses, a badge, a knit hat and a radio as similar to those possessed by the man who shot Lauretta.
Sandra Thomas next testified that she was in the living room on the evening of February 4, 1979. She heard a man on the front porch say that he was from the "State's Attorney's police" and heard a sound like police radio transmissions. When Robert opened the door she saw a man wearing a hat and silver wire-rimmed glasses holding a handgun. Sandra viewed the man through the open door for two to three seconds as he stepped into the house with one foot and fired the gun. On November 27, 1979, Sandra viewed a lineup and identified defendant as the man who shot Lauretta. In court she identified a hat and a pair of glasses as similar to those worn by the man on the porch and identified defendant as the man who fired the gun.
Joan Hullett concurred in the testimony of Robert and Sandra regarding the events of the evening of February 4, 1979. She did not see the man who fired the shot. She also testified that on January 19, 1979, two men came into her house at 5532 South La Salle and shot her husband, Joseph Hullett; he died the next day. Her daughter Lauretta witnessed the killing and was scheduled to testify on February 6, 1979, against the man she had identified in connection with that killing.
John Byrne, a Chicago police officer, testified that on the morning of February 5, 1979, Robert Thomas viewed two photograph displays, each consisting of five or six pictures. Neither display contained pictures of either the defendant or Roy Dixon, his brother. Robert identified no one in either display in connection with the killing of Lauretta Hullett. On February 10, 1979, Robert was shown a third display which contained pictures of both the defendant and Roy Dixon. From this display he selected a photograph of the defendant and identified him as the person who had shot Lauretta Hullett.
David O'Callaghan, also a police officer, testified that a pair of glasses, a black wallet containing a star-shaped badge, and a Motorola "beeper" were found in a hall closet at 5147 South Aberdeen and seized upon execution of a search warrant. A knit cap found in an upstairs bedroom was also seized.
The defense presented the following witnesses. Thomas Harris, the owner and manager of the restaurant where defendant was employed on February 4, 1979, testified that, to the best of his recollection, defendant worked his regular shift from 10 p.m. to 7 a.m. on *146 that date. The payroll records indicated that the defendant had not taken a day off during the pay period which included February 4, 1979. The records, however, showed only the total number of hours worked in a given week and did not show the number of hours worked each day. The total number of hours worked during the week in question was three hours less than it would have been if defendant had worked six eight-hour shifts as was the norm.
The defendant testified on his own behalf. He stated that he worked at the restaurant from 10 p.m. on February 4, 1979, until 7 the next morning, and that it takes approximately 1 1/2 hours to travel from his residence at 5147 South Aberdeen to the restaurant. He expressly denied going to the Hullett home on the evening in question, identifying himself as a State's Attorney's police officer, and shooting anyone. He stated that he kept all of his belongings in an upstairs bedroom of the Aberdeen residence and denied ever having seen the beeper radio, the wallet containing the star-shaped badge or the glasses recovered from 5147 South Aberdeen. He admitted owning several knit caps of the type recovered from that address.
The trial judge found defendant guilty of the murder of Lauretta Hullett, of burglary, and of home invasion. Defendant was sentenced to life imprisonment for murder. No sentence was imposed on the burglary or home invasion convictions.

OPINION
The first issue raised is whether reversible error resulted from the court's failure to obtain defendant's jury waiver for his sentencing hearing. Defendant contends that such failure deprived him of his constitutional right to a jury trial and asserts that he was, therefore, illegally sentenced. The State maintains that defendant suffered no prejudice as a result of the court's omission and argues that the error, if any, was harmless.
Initially, it is important to note that no issue is raised regarding defendant's waiver of his right to trial by jury. Defendant complains only that he did not waive his right to jury consideration in the separate sentencing hearing held to determine whether the death penalty should be imposed against him. The cases cited by defendant deal exclusively with waiver of the right to trial by jury and are, therefore, inapposite.
 1 The statute governing the imposition of the death penalty provides that, where requested by the State, the court shall conduct a separate sentencing proceeding (1) to determine the existence of circumstances under which imposition of a death sentence would be *147 proper, and (2) to consider any factors in aggravation and in mitigation. The proceeding shall be conducted before a jury or, if the defendant waives a jury, before the court alone. (Ill. Rev. Stat. 1981, ch. 38, par. 9-1(d)(3).) If the hearing is before a jury, the jury must first determine whether, on the circumstances before it, sufficient aggravating factors exist to warrant imposition of the death penalty. If this finding is negative then the court shall sentence the defendant to a term of imprisonment. If the jury finds that the death sentence may be imposed, it must then consider factors in aggravation and in mitigation. If the jury unanimously finds that there are no mitigating factors sufficient to preclude the imposition of the death sentence, the court shall impose such sentence. Otherwise, the court shall sentence the defendant to a term of imprisonment. (Ill. Rev. Stat. 1981, ch. 38, par. 9-1(g).) If the hearing is before the court alone, the court completes the same analysis in determining the sentence to be imposed.
 2 In the instant case if a jury had been impaneled, the result would have been a sentence of death or a sentence to a term of imprisonment. If the jury found sufficient aggravating factors to warrant imposition of the death penalty and insufficient factors to preclude imposition, the trial judge would have been required to sentence defendant to death. If the jury found insufficient aggravating factors to warrant imposition of the death penalty or mitigating factors sufficient to preclude it, in either such event, the trial judge would have been required to sentence defendant to a term of imprisonment. The latter determination was made in the instant case, albeit by the trial court alone, clearly with the result most favorable for defendant. Thus, given that the record evidences sufficient aggravating factors to warrant imposition of the death penalty, the only determination a jury could have made in the instant case which would have resulted in other than a sentence of imprisonment would have been a finding that there were no mitigating factors to preclude the imposition of the death sentence. In that case the court would have been required to sentence defendant to death.
While the trial court in the instant case did not obtain a waiver of jury for the sentencing hearing, such omission is not an error requiring vacation of the sentence where, as here, defendant has demonstrated no prejudice. See People v. Stephens (1973), 13 Ill. App.3d 642, 649, 301 N.E.2d 89.
 3 The next issue raised is whether defendant was improperly convicted for the offenses of burglary and home invasion. We recognize that a judgment of guilty in a criminal case is not final without a sentence (People v. Dixon (1982), 91 Ill.2d 346, 438 N.E.2d 180; People *148 v. Rose (1969), 43 Ill.2d 273, 253 N.E.2d 456) and thus is not appealable until a sentence is imposed (People ex rel. Filkin v. Flessner (1971), 48 Ill.2d 54, 268 N.E.2d 376). However, "where a case is properly on appeal from a final judgment on another offense, a reviewing court is empowered under Supreme Court Rule 366 (Ill. Rev. Stat. 1979, ch. 110A, par. 366(a)) to review the conviction of an offense for which no sentence was imposed and, upon affirming, to remand for sentencing." (People v. Zuniga (1981), 99 Ill. App.3d 396, 400, 425 N.E.2d 1094; People v. Scott (1977), 69 Ill.2d 85, 370 N.E.2d 540; see People v. Dixon.) This court, therefore, has jurisdiction to consider defendant's claim.
Defendant asserts that his conviction for the offenses of burglary and home invasion were based upon the same acts as the murder conviction. He argues that the convictions for the "lesser offenses" were, therefore, precluded by the murder conviction and must be vacated. The State maintains that burglary and home invasion are neither lesser-included offenses of murder, nor are they lesser-included offenses of each other. The State argues that although each offense stemmed from the series of acts engaged in to accomplish the murder, separate acts support each conviction and urges that this cause be remanded for sentencing on the burglary and home invasion convictions.
Following are the pertinent statutory provisions concerning each offense for which defendant was convicted:
"Sec. 19-1. Burglary. (a) A person commits burglary when without authority he knowingly enters * * * a building * * * with intent to commit therein a felony or theft." Ill. Rev. Stat. 1981, ch. 38, par. 19-1.
"Sec. 12-11. Home Invasion. (a) A person * * * commits home invasion when without authority he or she knowingly enters the dwelling place of another when he or she knows or has reason to know that one or more persons is present and
* * *
(2) Intentionally causes any injury to any person or persons within such dwelling place." Ill. Rev. Stat. 1981, ch. 38, par. 12-11.
"Sec. 9-1. Murder * * * (a) A person who kills an individual without lawful justification commits murder if, in performing the acts which cause the death:
(1) He either intends to kill or do great bodily harm to that individual or another, or knows that such acts will cause death to that individual or another; or
(2) He knows that such acts create a strong robability of *149 death or great bodily harm to that individual or another; * * *." Ill. Rev. Stat. 1981, ch. 38, par. 9-1(a).
 4 In People v. King (1977), 66 Ill.2d 551, 363 N.E.2d 838, cert. denied (1977), 434 U.S. 894, 54 L.Ed.2d 181, 98 S.Ct. 273, our supreme court abandoned the requirement that offenses be independently motivated in order to sustain multiple convictions and concurrent sentences (see People v. Scott (1977), 69 Ill.2d 85, 370 N.E.2d 540) and held that "when more than one offense arises from a series of incidental or closely related acts and the offenses are not, by definition, lesser included offenses, convictions with concurrent sentences can be entered." (People v. King (1977), 66 Ill.2d 551, 566, 363 N.E.2d 838.) An "act," as defined in King, is "any overt or outward manifestation which will support a different offense." (66 Ill.2d 551, 566, 363 N.E.2d 838.) Therefore, as long as there are multiple acts, their interrelationship does not preclude multiple convictions and the imposition of concurrent sentences. People v. Myers (1981), 85 Ill.2d 281, 288, 426 N.E.2d 535.
 5, 6 This court recently stated that for an offense to be a "lesser included offense, the greater offense must include every element in the lesser offense plus one or more elements; the lesser offense does not have any element that is not included in the greater one. In other words, it is impossible to commit the greater offense without necessarily committing the lesser also." (People v. Pavic (1982), 104 Ill. App.3d 436, 448, 432 N.E.2d 1074.) In Pavic we held that burglary requires a different mental element than does home invasion and therefore is not an included offense. (104 Ill. App.3d 436, 448, 432 N.E.2d 1074.) Examination of the requisite elements of each offense for which defendant was convicted reveals that no one of the offenses includes every element of any other of the offenses and, therefore, none are lesser-included offenses. Thus, defendant's interrelated acts adequately support multiple convictions and concurrent sentences.
 7 The third issue is whether defendant was sentenced in accordance with the provisions of the applicable statute. "The Unified Code of Corrections vests a wide discretion in sentencing judges in order to permit reasoned judgments as to the penalty appropriate to the particular circumstances of each case." (People v. La Pointe (1981), 88 Ill.2d 482, 492, 431 N.E.2d 344.) The trial court is normally the proper forum in which a suitable sentence is to be determined. The trial judge's decisions in regard to sentencing are entitled to great deference and weight (People v. Perruquet (1977), 68 Ill.2d 149, 154, 368 N.E.2d 882; People v. Willingham (1982), 89 Ill.2d 352, 364, 432 *150 N.E.2d 861) and will not be disturbed absent an abuse of discretion. People v. Gallardo (1983), 112 Ill. App.3d 764, 775, 445 N.E.2d 1213.
The statute provides that the sentence of imprisonment for the offense of murder shall be "(a) a term * * * not less than 20 years and not more than 40 years, or (b) if the court finds that the murder was accompanied by exceptionally brutal or heinous behavior indicative of wanton cruelty or that any of the aggravating factors listed in subsection (b) of Section 9-1 of the Criminal Code of 1961 are present, the court may sentence the defendant to a term of natural life imprisonment * * *." (Ill. Rev. Stat. 1981, ch. 38, par. 1005-8-1(a)(1).) One of the factors listed in subsection (b) of section 9-1 of the Criminal Code of 1961 is that the murdered individual was killed in the course of certain other felonies, one of which is burglary. (Ill. Rev. Stat. 1981, ch. 38, par. 9-1(b)(6).) The court here made an express finding that the instant murder was accompanied by exceptionally brutal and heinous behavior indicative of wanton cruelty and that the murdered individual was killed in the course of a burglary and sentenced defendant to a term of natural life imprisonment.
Defendant contends that he was illegally sentenced because (1) the burglary merged in the murder conviction and the killing, therefore, did not take place in the course of a separate and independent felony, and (2) the killing was not accompanied by brutal or heinous behavior. We will address the latter contention first. Defendant argues that since the killing was committed by firing a single shot his conduct therefore lacks characteristics necessary to categorize it as "exceptionally brutal or heinous behavior, indicative of wanton cruelty." Our supreme court has defined "heinous" as "`hatefully or shockingly evil: grossly bad: enormously and flagrantly criminal'"; "brutal" includes that which is "`grossly ruthless,' `devoid of mercy or compassion: cruel and cold-blooded.'" People v. La Pointe (1981), 88 Ill.2d 482, 501, 431 N.E.2d 344.
 8 Under the terms of the statute, in imposing sentence the court may consider the conduct which led up to the killing, not merely the single, discrete act which caused the death. (See La Pointe.) The record here shows that defendant, in a calculated and cold-blooded manner, planned and carried out the murder of an 18-year-old woman in her own home. He inspired trust and confidence in the occupants of the residence by deceptively holding himself out as a law enforcement officer and thereby gained entrance to the victim's home. When the door was opened to him he found his target and fired one shot which killed Lauretta Hullett. We do not believe that such behavior can be said to fall outside our supreme court's definition of "brutal" and *151 "heinous" simply because only one shot was fired. We agree with the trial court's characterization as a "hideous deception" defendant's misrepresentation of himself as a police officer in order to gain entrance to a private home for the purpose of killing a resident thereof. We are unable to say that the trial court abused its discretion in sentencing defendant to natural life imprisonment and, therefore, we will not disturb that sentence. Our determination on this matter renders unnecessary consideration of defendant's assertion that the burglary merged in the murder conviction. The sentence imposed was not improper regardless of whether the murder occurred in the course of another felony.
 9 The final issue for review is whether defendant was proved guilty beyond a reasonable doubt. In contending that he was not proved guilty beyond a reasonable doubt, defendant basically questions the credibility of the witnesses. In a trial without a jury it is the function of the trial court to determine the credibility of the witnesses, the weight to be given their testimony, and the inferences to be drawn from the evidence (People v. Akis (1976), 63 Ill.2d 296, 298, 347 N.E.2d 733), and where the evidence is merely conflicting a reviewing court may not substitute its judgment for that of the trier of fact (People v. Clark (1964), 30 Ill.2d 216, 219, 195 N.E.2d 631). A criminal conviction will not be reversed unless the evidence is so improbable as to raise a reasonable doubt of guilt. People v. Stringer (1972), 52 Ill.2d 564, 568, 289 N.E.2d 631.
 10-12 Defendant first argues that the identification made by Robert Thomas was questionable in that the viewing took place on a darkened porch and lasted only 30 seconds. It is undisputed that the testimony of one eyewitness is sufficient to convict, provided the witness is credible and the viewing of the accused was under such circumstances as would permit a positive identification (People v. Martin (1970), 47 Ill.2d 331, 334-35, 265 N.E.2d 685, cert. denied (1971), 403 U.S. 921, 29 L.Ed.2d 700, 91 S.Ct. 2240; People v. Clarke (1971), 50 Ill.2d 104, 110, 277 N.E.2d 866), even where that testimony is contradicted by the accused (People v. Stringer; People v. Yarbrough (1977), 67 Ill.2d 222, 367 N.E.2d 666). In the instant case Robert's identification of defendant was based upon his viewing of defendant as he stood on the porch of the Hullett home. The porch was illuminated by two street lights located nearby and by the light from inside the house. The light on the porch was sufficient to enable Robert to inspect the badge and identification card displayed to him, to determine that the picture on the card depicted the man on the porch and to read the words "state's attorney" on the card. Robert was able to *152 identify defendant in police photographs and in a lineup. The length of time a witness observes a defendant is only one factor to be considered and is not in itself determinative of whether there has been a positive identification. (See People v. Yarbrough.) Although Robert observed defendant for a period of only 30 seconds, his was not a casual viewing but rather an examination made with a heightened degree of attention as it was made for the specific purpose of trying to identify a man unknown to him seeking nighttime entrance to a private home where, only two weeks earlier, one of the residents had been murdered. On the witness stand Robert was asked to identify pictures of the defendant from among several other photographs he was shown. The trial judge noted that Robert, without looking toward the defendant, unhesitatingly selected the pictures of the defendant. It is our opinion that the record here presented supports a finding that the circumstances surrounding the viewing of the accused were such as to permit a positive identification.
Defendant next argues in support of his reasonable doubt contention that the testimony of Sandra Thomas was not credible due, principally, to the fact that she had only a short period of time within which to observe defendant. The fact that the period of observation was very short does not render the identification insufficient as a matter of law. (People v. Milam (1980), 80 Ill. App.3d 245, 251, 399 N.E.2d 703.) Rather, whether or not a witness had a good opportunity to observe the defendant goes to the weight to be given such identification and is a question for the trier of fact whose determination will not be overturned by a reviewing court unless so contrary to the evidence as to be unjustified. (Milam.) We need not engage in an extensive analysis of Sandra Thomas' testimony since the trial court heard the testimony of Robert Thomas, which testimony alone is sufficient to sustain a conviction. See People v. Yarbrough (1977), 67 Ill.2d 222, 226, 367 N.E.2d 666; People v. Martin (1970), 47 Ill.2d 331, 334-35, 265 N.E.2d 685.
 13, 14 Defendant further argues in support of his reasonable doubt contention that the identifications made by both Robert and Sandra were incredible, citing a minor difference in their descriptions of defendant's facial hair. In assessing the credibility of an identification the central concern is not whether there are discrepancies in witnesses' descriptions of a defendant but rather whether there existed an adequate opportunity for a witness to definitely identify the accused. (People v. Watkins (1981), 98 Ill. App.3d 889, 896, 424 N.E.2d 701; People v. Sanders (1976), 38 Ill. App.3d 473, 348 N.E.2d 229.) If so, the discrepancies do not destroy the validity of the identification *153 but go instead to the weight of the testimony (People v. Sanders) and are to be evaluated by the finder of fact (People v. Yarbrough). In the instant case we are unable to say that the trial court's determination as to defendant's guilt is so contrary to the evidence as to be unjustified and it, therefore, will not be disturbed.
Defendant's remaining contentions question the trial court's determination regarding testimony relating to his alibi defense and to the introduction of physical evidence. These contentions turn on the credibility of the witnesses. As stated above, we may not substitute our judgment for that of the trier of fact on questions concerning credibility of witnesses unless the evidence is so improbable as to raise a reasonable doubt of defendant's guilt. (People v. Manion (1977), 67 Ill.2d 564, 578, 367 N.E.2d 1313, cert. denied (1978), 435 U.S. 937, 55 L.Ed.2d 533, 98 S.Ct. 1513.) Upon careful examination of the entire record in this cause, we do not find this to be the case and must, therefore, resolve the remaining contentions against defendant.
 15, 16 Finally, defendant asserts that he received incompetent assistance of counsel. Our supreme court in a recent opinion held that the standard for effective assistance of counsel announced in People v. Greer (1980), 79 Ill.2d 103, 402 N.E.2d 203, should be applied in all cases involving either retained or appointed counsel. (People v. Royse (1983), 99 Ill.2d 163, 169-70, 457 N.E.2d 1217.) The Greer court stated that the inadequacy of a defendant's trial counsel entitles him to a new trial if the incompetence produced substantial prejudice to the defendant without which the result would probably have been different. (People v. Greer (1980), 79 Ill.2d 103, 120-21, 402 N.E.2d 203.) Effective assistance means competent, not perfect, representation. (People v. Berland (1978), 74 Ill.2d 286, 311, 385 N.E.2d 649, cert. denied (1979), 444 U.S. 833, 62 L.Ed.2d 42, 100 S.Ct. 63.) Defendant here contends that defense counsel engaged in questionable trial tactics by presenting to the trial court evidence regarding various aspects of the investigation of the murder of Joseph Hullett, and defendant's prior conviction for a misdemeanor. He argues that the introduction of such testimony made a fair evaluation of the evidence "difficult if not altogether impossible." By defendant's own admission the conduct complained of involved tactical decisions which will not be reviewed by this court. (People v. Gallardo (1983), 112 Ill. App.3d 764, 445 N.E.2d 1213; see People v. Greer.) Furthermore, a defendant who charges that his counsel was incompetent must establish both the actual incompetency and the resultant prejudice; charges of incompetency cannot be based solely upon assertions. (People v. *154 Ashley (1966), 34 Ill.2d 402, 411, 216 N.E.2d 126.) Defendant here merely asserts incompetence and fails to show that he was prejudiced in any way, certainly not to the extent that the outcome of his trial would have been different. See People v. Moore (1981), 102 Ill. App.3d 651, 658-59, 429 N.E.2d 1312.
For the foregoing reasons, the conviction and sentence imposed for murder are affirmed; the convictions for burglary and home invasion are affirmed and remanded for sentencing thereon.
Affirmed and remanded in part for sentencing.
LORENZ and O'CONNOR, JJ., concur.
