Determine which of the following sinusoids are periodic and compute their fundamental period. (a) cos0.01πn (b) cos(π 30n/105) (c) cos3πn (d) sin3n (e) sin(π 62n/10)
Determine whether or not each of the following signals is periodic. In case a signal is periodic, specify its fundamental period. (a) xa(t) = 3 cos(5t + π/6) (b) x(n) = 3 cos(5n + π/6 ) (c) x(n) = 2exp[j(n/6 − π)] (d) x(n) = cos(n/8) cos(π n/8) (e) x(n) = cos(π n/2) − sin(π n/8) + 3cos(π n/4 + π/3)
Consider the following analog sinusoidal signal: xa(t) = 3sin(100πt) (a) Sketch the signal xa(t) for 0 ≤ t ≤ 30 ms. (b) The signal xa(t) is sampled with a sampling rate Fs = 300 samples/s. Determine the frequency of the discrete-time signal x(n) = xa(nT), T = 1/Fs, and show that it is periodic. (c) Compute the sample values in one period of x(n). Sketch x(n) on the same diagram with xa(t). What is the period of the discrete-time signal in milliseconds? (d) Can you find a sampling rate Fs such that the signal x(n) reaches its peak value of 3? What is the minimum Fs suitable for this task?
An analog signal contains frequencies up to 10 kHz. (a) What range of sampling frequencies allows exact reconstruction of this signal from its samples? (b) Suppose that we sample this signal with a sampling frequency Fs = 8 kHz. Examine what happens to the frequency F1 = 5 kHz. (c) Repeat part (b) for a frequency F2 = 9 kHz.
An analog electrocardiogram (ECG) signal contains useful frequencies up to 100 Hz. (a) What is the Nyquist rate for this signal? (b) Suppose that we sample this signal at a rate of 250 samples/s. What is the highest frequency that can be represented uniquely at this sampling rate?
An analog signal xa(t) = sin(480πt) + 3sin(720πt) is sampled 600 times per second. (a) Determine the Nyquist sampling rate for xa(t). (b) Determine the folding frequency. (c) What are the frequencies, in radians, in the resulting discrete time signal x(n)? (d) If x(n) is passed through an ideal D/A converter, what is the reconstructed signal ya(t)?