Test: Discrete Time Signal Analysis - 2 - Electronics and Communication Engineering (ECE) MCQ

Explanation: We know that,

Explanation: We know that, if a signal x(n) is real, then
X*(ω)=X(-ω)
If the signal is even symmetric, then the magnitude on both the sides should be equal.
So, |X*(ω)|=|X(-ω)| =>| X(-ω)|=| X(ω)|.

Explanation: Since |a|<1, the sequence x(n) is absolutely summable, as can be verified by applying the geometric summation formula.

Explanation: The Fourier transform of this signal is

Explanation: Let us consider the signal to be x(n)

Explanation: The given x(n) do not have Z-transform. But the sequence have finite energy. So, the given sequence x(n) has a Fourier transform.

Explanation: Let us consider a sequence x(n) having a z-transform X(z). We assume that x(n) is a stable sequence so that X(z) converges on to the unit circle. The complex cepstrum of the signal x(n) is defined as the sequence cx(n), which is the inverse z-transform of Cx(z), where Cx(z)=ln X(z)
=> cx(z)= X^-1(ln X(z))

Explanation: We know that,

Explanation: Given x(n)=u(n)
We know that the z-transform of the given signal isROC:|z|>1
X(z) has a pole p=1 on the unit circle, but converges for |z|>1.
If we evaluate X(z) on the unit circle except at z=1, we obtain

Explanation: We know that, for a low frequency signal, the power signal has its power density spectrum concentrated about zero frequency.

Explanation: T he anti aliasing filter is an analog filter which has a twofold purpose. First, it ensures that the bandwidth of the signal to be sampled is limited to the desired frequency range. Using an anti aliasing filter is to limit the additive noise spectrum and other interference, which often corrupts the desired signal. Usually, additive noise is wide band and exceeds the bandwidth of the desired signal.

Explanation: Analog signal processing operations cannot be done very precisely either, since electronic components in analog systems have tolerances and they introduce noise during their operation. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.

Explanation: In addition to the relatively broad frequency domain classification of signals, it is often desirable to express quantitatively the range of frequencies over which the power or energy density spectrum is concentrated. This quantitative measure is called the ‘bandwidth’ of a signal.

Explanation: If the difference in the cutoff frequencies is much less than the mean frequency, the such a band pass signal is known as narrow band signal.

Explanation: Electroencephalogram(EEG) signal has a frequency range of 0-100 Hz.