English
Menu

Digital Signal Processing Basics

At a sampling frequency of 8 kHz, a moving-average filter y[n] = (x[n] + x[n − 1] + … + x[n − 7])/8 averages the latest 8 samples. Which of the following is the lowest frequency at which its output is 0?

  1. A500 Hz
  2. B1 kHz
  3. C4 kHz
Show answer and explanation

Answer: B. 1 kHz

The gain of an N-sample moving average is (1 + 1 + … + 1)/N = 1 at DC, and it is 0 at integer multiples of fs/N (other than DC). A sine wave at fs/N = 8000 ÷ 8 = 1 kHz completes exactly one cycle in 8 samples, so its average is 0. The moving average is a simple low-pass filter, but it has side lobes where the gain rises again between the nulls, so its cutoff is not very steep.

  • A. This is fs/(2N) = 8000 ÷ 16. The first null is at fs/N.
  • B. Correct. At 1 kHz one cycle takes 8 samples, so the average is 0.
  • C. This is the Nyquist frequency. The output is 0 here too, but the lowest null is at 1 kHz.
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. Which of the following gives the gains at DC and at the Nyquist frequency of the first-order IIR low-pass filter given by the exponential smoothing y[n] = 0.2x[n] + 0.8y[n − 1]?
  2. Which of the following correctly describes the bilinear transform used to design a digital filter from the transfer function H(s) of an analog filter?
  3. Which of the following is a correct precaution when implementing a high-order IIR filter in fixed point with coefficients of limited bit width?
  4. A signal sampled at 48 kHz is reduced to 12 kHz by keeping one sample out of every four (decimation by 4). Which of the following frequency components should the low-pass filter placed before the downsampling remove?
  5. To raise the sampling frequency by a factor of L, L − 1 zeros are inserted between successive samples (zero insertion). Which of the following correctly describes the processing needed next?