# A voice signal is band-limited to 3.3 kHz. What is the Nyquist frequency?

I'm having a some trouble with an assignment I have to do. I don't come from electrical engineering background and would appreciate any help I can get.

"A voice signal is band-limited to 3.3 kHz. What is the Nyquist frequency? It is sampled using a guard band of 1.4 kHz is applied and converted to digital data with 7 bits per sample. What is the resulting data rate?"

I calculated the Nyquist frequency using the formula $$f_{Ny} = \frac{1}{2}f_s = \frac{1}{2}3300\text{ Hz} = 1650\text{ Hz}.$$

Is this correct? Moving along I have no idea how to do the last part of the question, my lecturer didn't have any examples of this type of question so I'm really lost. Or else if someone could point me to a source that will show me how to do this question, that would be great too.

• The "data rate" part of the question should be fairly straightforward: once you know how many samples per second you're taking, and how many bits you have per sample, you can easily find how many bits per second you're producing.
– MBaz
Apr 24, 2018 at 21:48

## 1 Answer

If an analog signal is limited in frequency, and $W$ is its highest frequency component, then the minimum sampling frequency to avoid time-aliasing is $f_s = 2W$.

The Nyquist frequency is half the sampling rate of the system.

In your case, and to avoid time-aliasing, the Nyquist frequency would be $f_{Nyquist} = 3 300\text{ Hz}$. But, since an additional guard band is considered, then the Nyquist frequency is:

$$f_{Nyquist} = 3 300\text{ Hz} + 1 400\text{ Hz} = 4 700\text{ Hz}$$

• Okay I understand. But isn't there a difference between Nyquist frequency and Nyquist rate? I say this because I read this when I was researching "The Nyquist frequency should not be confused with the Nyquist rate, which is the minimum sampling rate that satisfies the Nyquist sampling criterion for a given signal or family of signals." - Wiki Apr 24, 2018 at 21:26
• The Nyquist frequency is half of the sampling rate of a discrete signal processing system. The Nyquist rate is twice the bandwidth of a bandlimited function or a bandlimited channel. Apr 24, 2018 at 21:31
• Not quite bad enough for a downvote, but for anything finite length (e.g. that exist in the real universe), the sampling rate must be greater than twice the band-limit, not = 2W. Apr 24, 2018 at 21:36
• @cod3min3 See here for a definition of Nyquist frequency and Nyquist rate. Following the most common convention, your question should have asked for the "Nyquist rate".
– MBaz
Apr 24, 2018 at 21:40