Consider a continuous-time finite-energy signal  whose Fourier transform vanishes outside the frequency interval , where  is in .

The signal  is uniformly sampled to obtain . Here,

with  being the Dirac impulse, , and . The sampled signal  is passed through an ideal lowpass filter  with cutoff frequency  and passband gain .

The output of the filter is given by ___________.

A continuous time signal is sampled at a rate of 15 Hz. The sampled signal  when passed through an LTI system with impulse response        

Produces an output The expression for is __________.

Let  and  be two band-limited signals having bandwidth  each. In the figure below, the Nyquist sampling frequency, in , required to sample , is

Consider a real-valued base-band signal , band limited to . The Nyquist rate for the signal  is

A band limited low-pass signal x(t) of bandwidth 5kHz is sampled at a sampling rate . The signal x(t) is reconstructed using the reconstruction filter H(f) whose magnitude response is shown below:

The minimum sampling rate f, (in kHz) for perfect reconstruction of x(t) is _______

The signal , where t is in seconds, is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal lowpass filter with frequency response H (f) as follows:  

What is the number of sinusoids in the output and their frequencies in kHz?

A continuous-time function x(t) is periodic with period T. The function is sample uniformly with a sampling period  In which one of the following cases is the sampled signal periodic?

A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed through an ideal analog low pass filter with a cut-off frequency of 23 Hz. The fundamental frequency (in Hz) of the output is____________

A continuous-time filter with transfer function  is converted to a discrete-time filter with transfer function  so that the impulse of the continuous-time, sampled at 2Hz, is identical at the sampling instants to the impulse response of the discrete time filter. The value of k is ___________.

Consider the signal, where t is in seconds. The Nyquist sampling rate (in samples/second) for the signal y(t) = x(2t + 5) is

The signal  is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response. The filter output is

Consider a continuous-time signal defined as .

Where ‘∗’ denotes the convolution operation and t is in seconds. The Nyquist sampling rate (in samples/sec) for x(t) is _____.

Consider two real values signals, x(t) band-limited to
[-500Hz, 500Hz] and y(t) band limited to [-1kHz, 1kHz].

For, the Nyquist sampling frequency (in kHz) is _______.

Let be sampled at 20 Hz and reconstructed using an ideal low-pass filter with cut-off frequency of 20 Hz. The frequency/frequencies present in the reconstructed signal is/are

The Nyquist sampling rate for the signal  is given by

An LTI system having transfer function  and input  is in steady state. The output is sampled at a rate rad/s to obtain the final output {y(t)}. Which of the following is true?

A 1 KHz sinusoidal signal is ideally sampled at 1500 samples/sec and the sampled signal is passed through an ideal low-pass filter with cut-off frequency 800 Hz. The output signal has the frequency

A band limited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples through

A band-limited signal x(t) with a spectrum X(f) as shown in Figure (a) is processed as shown in Figure (b). p(t) is a periodic train of impulses as in Figure (c). The ideal band-pass filter has a pass band from 26 KHz to 34 KHz.

(a) Calculate the Fourier series coefficients  in the Fourier expansion of p(t) in the form

(b) Find the Fourier Transform of p(t)

(c) Obtain and sketch the spectrum of .

(d) Obtain and sketch the spectrum of y(t).        

(a)

(b)

(c)

A signal has frequency components from 300 Hz to 1.8 KHz. The minimum possible rate at which the signal has to be sampled is _________Hz.