======================================================================= ss15_A00-1 (Key Concept of Signals and Systems) ----------------------------------------------------------------------- SS1-SS-3: Signals and Systems For the functions used to describe the signals, the time axis is absolute value, i.e., the world time, (a) True or (b) False and for the functions used to describe the systems, the time axis is relative value, i.e., the time difference from the activation time? (c) True or (d) False (a) True (c) True ======================================================================= ss15_A01-1 (DT Signals and CT Signals) ----------------------------------------------------------------------- SS1-SS-7: DT Signals and CT Signals The time variables for CT signals is real number, i.e., x(t), t is real number (the R set), (a) True or (b) False and the time variables for DT signals is integer number, i.e., x[n], n is integer number (the Z set), (c) True or (d) False (a) True (c) True ======================================================================= ss15_A01-2 (Signal Energy & Signal Power) ----------------------------------------------------------------------- SS1-SS-11: Signal Energy & Signal Power (a) If the total energy of one signal over an infinite time interval is finite, say, 10, then, what is the average power of the signal, over an infinite time interval? (b) If the average power of one signal over an infinite time interval is finite, say, 10, then, what is the total energy of the signal, over an infinite time interval? (a) 0 (b) infinity ======================================================================= ss15_A02-1 (Transformation of Signals) ----------------------------------------------------------------------- SS1-SS-13: Delayed and Advanced Signals (a) For a signal x(t), the 3.4-unit delayed signal becomes x(t-3.4), i.e., to the left of the original signal x(t)? (b) For a signal x(t) or x[n], a 2-unit advanced signal becomes x[n+2], i.e., to the right of the original signal x[n]? (a) No. To the right of the original signal x(t). (b) No. To the left of the original signal x[n]. ----------------------------------------------------------------------- SS1-SS-15: Time Scaling For x(t), the shape of x(3t) becomes wider than that of x(t)? (a) True or (b) False (b) No. Narrower. ======================================================================= ss15_A02-2 (Example of Transforming Signals) ----------------------------------------------------------------------- SS1-SS-18: x( A t + B) For x(t), (a) what is the signal after doing the following steps: (1) t -> t + 2 (2) t -> t/3 e.g., x( A t + B), what are A and B? (b) what is the singal after doing the following steps: (1) t -> t/3 (2) t -> t + 2 e.g., x( A t + B), what are A and B? (a) A = 1/3, B = 2. (b) A = 1/3, B = 2/3. ======================================================================= ss15_A02-3 (Periodic Signals) ----------------------------------------------------------------------- SS1-SS-20: Periodic Signals Is x[n] = cos(n/8 - pi) a periodic signal? (a) Yes or (b) No (b) No. The possible period is N0 = 16 pi and it is impossible because N0 should be an integer. ======================================================================= ss15_A02-4 (Even-Odd Signals) ----------------------------------------------------------------------- SS1-SS-25: Even-Odd Signals Let x[n] = 1, n < 0 x[n] = 2, n = 0 x[n] = 1, n > 0 Find the even part and odd part of x[n]. The defined x[n] is an even signal and then the even part of x[n] is x[n] and the odd part of x[n] is 0 for all n. ======================================================================= ss15_A03-1 (CT Complex Exponential Signals) ----------------------------------------------------------------------- SS1-SS-28: Euler's relation What is the Euler's relation? e^(j theta ) = cos( theta ) + j sin( theta ) ======================================================================= ss15_A03-2 (Period Frequency Energy Power) ----------------------------------------------------------------------- SS1-SS-34: Euler's relation Which ones(s) is/are true? (1) cos( theta ) = ( e^(j theta) + e^(- j theta) ) /2j (2) cos( theta ) = ( e^(j theta) + e^(- j theta) ) /2 (3) cos( theta ) = ( e^(j theta) - e^(- j theta) ) /2j (4) cos( theta ) = ( e^(j theta) - e^(- j theta) ) /2 (5) sin( theta ) = ( e^(j theta) + e^(- j theta) ) /2j (6) sin( theta ) = ( e^(j theta) + e^(- j theta) ) /2 (7) sin( theta ) = ( e^(j theta) - e^(- j theta) ) /2j (8) sin( theta ) = ( e^(j theta) - e^(- j theta) ) /2 (2) (7) ----------------------------------------------------------------------- SS1-SS-35: Total energy & average power What is total energy (E) & average power (P) of e^( j 4 pi t) over a time interval (2 pi)? (1) E = 1 (2) E = 2 (3) E = 2 pi (4) E = 4 pi (5) P = 1 (6) P = 2 (7) P = 2 pi (8) P = 4 pi (3) (5) ======================================================================= ss15_A03-3 (CT General Complex Exponential Signals) ----------------------------------------------------------------------- SS1-SS-36: CT basic exponential signals Is e^( j k w_0 t ), k=0, +-1, +-2, ... a set of harmonically related periodic exponentials? (a) Yes or (b) No (a) Yes ======================================================================= ss15_A03-4 (DT Complex Exponential Signals) ----------------------------------------------------------------------- SS1-SS-36: DT basic exponential signals ======================================================================= ss15_A03-5 (Periodicity Properties of DT Complex Exponentials) ----------------------------------------------------------------------- SS1-SS-44: Periodicity of DT exponentials For x[n] = e^( j w0 n ), w0 = (2pi)/(5), (a) Show that: x[n] is periodic with respect to n, and what is this period? (b) Show that: x[n] is periodic with respect to w0, and what is this period? (c) What values of w0 are high frequencies? (a) e^( j w0 (n+N) ) = ... = e^( j w0 (n) ) and then ( 2pi/5 )*N = (2pi)*k, k some integer. N = 5, 10, 15,... (b) e^( j (w0+W) n ) = ... = e^( j w0 (n) ) and then (W)*n = k*(2pi). W = 2pi, 4pi, 6pi,... (c) w0 = +-pi, +-3pi, +-5pi, ... ======================================================================= ss15_A03-6 (CT & DT Exponential Signals) ----------------------------------------------------------------------- SS1-SS-45: CT and DT exponential signals For x(t) = cos( w0 t ), when w0 is larger, the frequency of x(t) is higher? (a) Ture or (c) False For x[n] = cos( w0 n ), when w0 is larger, the frequency of x[n] is higher? (c) Ture or (d) False (a) Yes (d) No ======================================================================= ss15_A03-7 (Periodicity Properties Comparison of CT & DT Signals) ----------------------------------------------------------------------- SS1-SS-53: Periodicityof DT signals What is the period of x(t) = cos( 6 pi t / 23 )? What is the period of x[n] = cos( 6 pi n / 23 ) (a) T = 23/3 (b) N = 23 ======================================================================= ss15_A04-1 (DT Unit Impulse & Unit Step Sequences) ----------------------------------------------------------------------- SS1-SS-60: Sample by Unit Impulse x[n] delta[n+3] is equal to: (a) x[3] delta[n-3] (b) x[-3] delta[n-3] (c) x[3] delta[n+3] (d) x[-3] delta[n+3] (d) ======================================================================= ss15_A04-2 (CT Unit Impulse & Unit Step Functions) ----------------------------------------------------------------------- SS1-SS-64: Relationship Between Impulse & Step u(t) = integrate_0^infinity delta( t - tau ) (d tau)? (a) True or (b) False (a) True ======================================================================= ss15_A05-1 (Physical Systems & Examples) ----------------------------------------------------------------------- SS1-SS-71, 73: CT and DT Systems For a CT system, the change of the output signal is a function of the input signal? (a) True or (b) False? For a DT system, the change of the output signals at different time instants is a function of the input signal? (c) True or (d) False? (a) Yes (c) Yes ======================================================================= ss15_A05-2 (Interconnections of Systems) ----------------------------------------------------------------------- SS1-SS-77: Feedback Interconnection For two systems interconnected by a standard feedback loop, x2 is a function of y1 and x1 is a function of y2? (a) Yes or (b) No (a) Yes ======================================================================= ss15_A06-1 (Memory Invertibility) ----------------------------------------------------------------------- SS1-SS-79: Memory y[n] = (n-1) x[n] is a system with memory? (a) Yes or (b) No (b) No ----------------------------------------------------------------------- SS1-SS-80: Inverse What is the inverse system of y[n] = x[n-1]? w[n] = [n+1] ======================================================================= ss15_A06-2 (Causality Stability) ----------------------------------------------------------------------- SS1-SS-81: Causal y(t) = cos(t+1) x(t-1) is a causal system? (a) Yes or (b) No (a) Yes ----------------------------------------------------------------------- SS1-SS-82: Stable y(t) = cos(t+1) x(t-1) is a stable system? (a) Yes or (b) No (a) Yes ======================================================================= ss15_A06-3 (Time Invariance Linearity) ----------------------------------------------------------------------- SS1-SS-84: Time-invariant y[n] = sin( x[n-1] ) is a time-invariant system? (a) Yes or (b) No (a) Yes ----------------------------------------------------------------------- SS1-SS-87: Linear y[n] = (n) x[n-1] is a linear system? (a) Yes or (b) No (a) Yes ======================================================================= -----------------------------------------------------------------------