FFT related question - Please help

Could some DSP guru please clarify some ideas that I have ? Suppose
that I am sampling some signal at some frequency fs. The sampled bytes
get collected in a buffer (max buffer size is some power of 2). Let us
suppose that I sample for some time and collect enough samples to
completely fill up the buffer.

As the sampling frequency is fs, I collect f samples per second, and
so the time required to collect to all the samples in my buffer is
total sample size divided by the sampling frequency.

Now suppose that I am sampling some audio signal and so the the lowest
audio frequency that I can capture will be the inverse of the time
period calculated above. That is, if I were to compute a FFT using the
sampled data, the harmonics, or peaks would correspond to the
multiples of this base frequency. If so, why bother computing the FFT,
since we can determine what frequencies we have captured simply by the
reasoning given above, and by extension, we can capture any frequency
in the audio range by varying the sampling frequency.

What are the flaws in this argument ? Any hints, suggestions would be
greatly appreciated, and thank you in advance for your help.

cpptutor2000@yahoo.com wrote:
(snip)

> Now suppose that I am sampling some audio signal and so the the lowest
> audio frequency that I can capture will be the inverse of the time
> period calculated above. That is, if I were to compute a FFT using the
> sampled data, the harmonics, or peaks would correspond to the
> multiples of this base frequency. If so, why bother computing the FFT,
> since we can determine what frequencies we have captured simply by the
> reasoning given above, and by extension, we can capture any frequency
> in the audio range by varying the sampling frequency.

You know the frequencies, but not the amplitude of each.

> What are the flaws in this argument ? Any hints, suggestions would be
> greatly appreciated, and thank you in advance for your help.

Well, the FFT doesn't tell you the frequencies anyway, you have to
know them already, just in the way you say.

-- glen

cpptutor2000@yahoo.com wrote:
> Could some DSP guru please clarify some ideas that I have ? Suppose
> that I am sampling some signal at some frequency fs. The sampled bytes
> get collected in a buffer (max buffer size is some power of 2). Let us
> suppose that I sample for some time and collect enough samples to
> completely fill up the buffer.
> 
> As the sampling frequency is fs, I collect f samples per second, and
> so the time required to collect to all the samples in my buffer is
> total sample size divided by the sampling frequency.
> 
> Now suppose that I am sampling some audio signal and so the the lowest
> audio frequency that I can capture will be the inverse of the time
> period calculated above. That is, if I were to compute a FFT using the
> sampled data, the harmonics, or peaks would correspond to the
> multiples of this base frequency. If so, why bother computing the FFT,
> since we can determine what frequencies we have captured simply by the
> reasoning given above, and by extension, we can capture any frequency
> in the audio range by varying the sampling frequency.
> 
> What are the flaws in this argument ? Any hints, suggestions would be
> greatly appreciated, and thank you in advance for your help.

What is in buffer depends on the signal. Suppose it is silence. Suppose 
it is a pure tone. Suppose it is a complex waveform. According to your 
supposition, all would have the same transform.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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