Test on Digital Signal Processing: DFT and FFT

Question 1: Incoherent sampling results in a DFT spectrum that is free from leakage.

A. Ano

B. Ne

Explanation: When sampling is incoherent, the relative frequency F of the signal is not an integer number, which causes so-called leakage in the DFT spectrum.

Question 2: A normalized window is used in DFT processing to correct the amplitudes of the spectral coefficients.

A. Ano

B. Ne

Explanation: Most windows are not normalized, meaning their weight is not unity, which results in incorrect amplitudes. Therefore, a normalized variant of the window is used to correct these amplitudes.

Question 3: According to the study materials, what is the effect of artificially increasing the signal segment length using zero padding in DFT analysis?

A. It decreases the overall impression of the spectrum image.

B. It provides a DTFT estimate with lower resolution.

C. It extends the signal segment by adding zeros.

D. It results in a DTFT estimate with higher resolution.

Explanation: The study materials state that 'The length of the segment can be artificially increased by so called zero padding – extending the signal segment by zeros.' (Option 2 is correct). It also explains that 'The second expression gives DTFT estimate with higher resolution' when zero padding is used (Option 3 is correct). Zero padding does not decrease the impression of the spectrum or provide lower resolution; it improves resolution.

Question 4: When performing Fourier filtering using the Fast Fourier Transform (FFT) to calculate convolution, what method is explicitly stated in the study materials to prevent circular convolution?

A. By applying a Hamming window to the signal segments.

B. By increasing the sampling frequency of the original signal.

C. By performing zero padding of sufficient length to the signals.

D. By using a shorter segment length N for the FFT calculation.

Explanation: The study materials state directly under 'Preventing Circular Convolution' that 'Circular convolution can be prevented by zero padding of sufficient length'.

Question 5: The second provided diagram illustrates overlapping segments, where Segment 1 starts at 0 and extends to 4096.

A. Ano

B. Ne

Explanation: The study material shows a diagram with 'Segment 1 Segment 2 Segment 3 Segment 4' where Segment 1 spans from 0 to 4096, and subsequent segments like Segment 2 begin at 2048, indicating an overlap.