English
Menu

Digital Signal Processing Basics

A signal sampled at 48 kHz is analyzed with a 1024-point discrete Fourier transform (DFT). Which of the following is the spacing of the frequency bins?

  1. AAbout 23.4 Hz
  2. BAbout 46.9 Hz
  3. CAbout 93.8 Hz
Show answer and explanation

Answer: B. About 46.9 Hz

The bin spacing of an N-point DFT is Δf = fs/N, and 48000 ÷ 1024 = 46.875 Hz ≈ 46.9 Hz. Bin k corresponds to the frequency k × Δf: k = 0 is DC and k = N/2 = 512 is the Nyquist frequency of 24 kHz. Δf is also the reciprocal of the observation time T = N/fs ≈ 21.3 ms, so finer bins require a longer observation time.

  • A. This is fs/(2N) = 24000 ÷ 1024. The bin spacing is fs/N.
  • B. Correct. 48000 ÷ 1024 = 46.875 Hz.
  • C. This divides fs by the number of positive-frequency bins, N/2 = 512 (48000 ÷ 512).
Practice this topic Back to topic

Books on Digital Signal Processing Basics Ad

As an Amazon Associate I earn from qualifying purchases.

More Digital Signal Processing Basics questions

  1. Let k = 0 be the DC bin. When a 1 kHz sine wave sampled at 8 kHz is analyzed with a 256-point DFT, which of the following is the index k of the bin where the peak appears on the positive-frequency side?
  2. A 64-point DFT of a real signal x[n] gives X[10] = 3 + 4j. Which of the following is X[54]?
  3. The DFT of the 8-point real signal x[n] = {3, 1, 3, 1, 3, 1, 3, 1} is defined as X[k] = Σx[n]e^(−j2πkn/8). Which of the following is the value of X[4], the bin at the Nyquist frequency?
  4. Suppose an N-point DFT takes about N² operations when computed from its definition and about N log₂N operations with the FFT (fast Fourier transform). For N = 1024, which of the following is closest to the reduction in the number of operations achieved by the FFT?
  5. A 256-point signal is followed by 768 zeros (zero padding) and a 1024-point DFT is computed. Compared with computing the DFT of the 256 points as they are, which of the following is correct?