what is an audio signal bandwidth and Nyquist rate?

Hi

Can anyone please help me to write the code to find the bandwidth and Nyquist rate of a speech signal?

Based on my research, I think I have to use fft function but I don't know how!

I appreciate it if you could write down the matlab codes required to find the bandwidth and Nyquist rate of a speech signal.

Thanks in advance.

Answer 1

[Star Strider]

Your Question leaves some details undefined.

However:

You choose the sampling frequency of your speech signal (ideally 44.1 kHz). See the documentation for audiorecorder for details.

The sampling interval is the inverse of that: Ts = 1/Fs;

The Nyquist frequency (usually Fn) is one-half the sampling frequency, Fn = Fs/2;. For reasons I won’t go into here, it is the highest uniquely resolvable frequency of a sampled signal.

Bandwidth of a speech signal varies, but for engineering purposes is considered to be 6 kHz.

The R2015a documentation for fft clearly explains what you need to do to calculate and plot it. Note specifically the code between the top two plot figures.

Of note, the 44.1 kHz sampling frequency is used because the upper limit of normal human hearing is about 20 kHz. The relevant Nyquist frequency slightly exceeds that.

[John BG]

The Nyquist frequency for a given signal is the frequency below which Alias happens [CARLSON]. Theoretically, if you sample above double the highest frequency component of a signal, there should be no Aliasing.

Your comment 'The relevant Nyquist frequency slightly exceeds that' reads as if there is more than one Nyquist frequency for high quality audio, which is not correct.

'normal human hearing' does not get 20kHz audio signals. Only a few exceptional ears may perceive harmonics above 15kHz. To play it safe, if the smartest ear ever known caught 19kHz tone, the standard will play it safe, put that audio signals audio frequency contents may reach 20kHz, the Nyquist frequency is 40kHz, and then you always oversample, get away from the Nyquist frequency, upwards, when producing Aliasing is not desired.

the 'normal human hearing' has enough with 3kHz, so to play it safe again the standard high quality sampling frequently is 44kHz, just for the sake of having more than just 2 time samples per cycle of the highest frequency component, the highest FFT bin.

Hope it helps

John

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[Star Strider]

Wrong.

The Nyquist frequency is the highest uniquely resolvable frequency in a sampled signal. Hardware anti-aliasing filters in ADCs prevent frequencies higher than the Nyquist frequency from being sampled.

The highest human hearing frequencies are on the order of 20 kHz. (Mine was such when I entered Medical School.) Those are generally in young people who have not frequently been exposed to loud sounds, and so do not have high frequency hearing loss.

For the record, I'm a Board Certified Internal Medicine Physician, and M.S. Biomedical Engineer.

[Image Analyst]

I think the Nyquist rate is 1 & 1/4-miles in 2:01.31, as was shown just a few hours ago. http://www.cnn.com/2016/05/07/horseracing/kentucky-derby/index.html

[Star Strider]

@Image Analyst — Brilliant!