ECT 303 -Digital Signal Processing

Which of the following statements is true regarding the Z-transform in signal processing?

• It is used to analyze continuous-time signals

• It provides a frequency-domain representation of discrete-time signals

• It is limited to analyzing linear time-invariant systems

• It is primarily used for analog signal processing

What is the significance of the Nyquist-Shannon sampling theorem in signal processing

• It defines the relationship between time and frequency domains

• It ensures that a continuous signal can be perfectly reconstructed from its samples

• It determines the maximum frequency that can be accurately represented in a sampled signal

• It specifies the minimum sampling rate required to prevent aliasing

In the context of signal processing, what does the term "Aliasing" refer to?

• Distortion caused by quantization errors

• Loss of high-frequency components during sampling

• Overlapping of frequency components in the spectrum

• ntroduction of noise in the signal

Which of the following statements accurately describes the relationship between the Discrete Fourier Transform (DFT) and the Discrete-Time Fourier Transform (DTFT)?

• The DFT is a sampled version of the DTFT

• The DTFT is a sampled version of the DFT

• The DFT is a continuous function while the DTFT is discrete

• The DTFT is defined for finite-length sequences only
  

When applying the circular convolution operation using the DFT, what is the significance of zero-padding the input sequences?

• It reduces the computational complexity of the convolution

• It ensures that the circular convolution result is equivalent to linear convolution

• It eliminates the need for frequency domain multiplication

• It introduces additional frequency components in the spectrum

When computing the Inverse Discrete Fourier Transform (IDFT) using Radix-2 FFT algorithms, what is a key consideration for efficient computation?

• Utilizing zero-padding in the time domain

• Applying windowing functions to the frequency domain

• Exploiting the symmetry properties of the input sequence

• Implementing overlap-add methods for block processing

What is the primary advantage of using FFT algorithms for computing the Discrete Fourier Transform (DFT) of real sequences?

• Reduced memory requirements

• Improved numerical accuracy

• Faster computation compared to direct methods

• Ability to handle non-linear phase signals

When applying FFT algorithms for the efficient computation of DFT, what role does the Decimation in Frequency approach play?

• It reduces the number of required FFT points

• It simplifies the computation of complex conjugates

• It optimizes the ordering of input data for FFT processing

• It minimizes the number of required FFT stages

In the context of digital signal processing, what is a key advantage of using FFT algorithms for spectral analysis compared to traditional methods?

• Improved time-domain resolution

• Ability to handle non-stationary signals

• Reduced computational complexity for long data sequences

• Enhanced frequency resolution with minimal processing overhead

What is the primary advantage of using Radix-2 decimation in time FFT algorithms for computing the FFT of real sequences compared to other FFT approaches?

• Reduced memory requirements

• Improved numerical accuracy

• Ability to handle non-linear phase signals

• Faster computation due to optimized butterfly operations