[sdiy] Digital filtering question

[Thomas Strathmann]

On 8/24/10 00:37 , cheater cheater wrote:
>> Firstly, it is more helpful to think of the the sinc function as:
>> sin(pi*x*n) / (pi*x*n)
>>
>> Where n is the sample number and x is the "design parameter" that is used to
>> dilate the sinc function in the time domain and control the cutoff frequency
>> in the frequency domain.
>>
>>> My question is: What's the cutoff frequency?
>>
>> The cutoff frequency is equal to the Nyquist frequency of the system (Fs/2)
>> divided by the number of samples between zero crossings in the sinc
>> function.   The number of samples between the zero crossings in the sinc
>> function is equal to 1/x in the above equation.
>
> Between which zero crossings? The sin(x)/x function has infinitely many.

It should be the first (two) zero crossing(s) because for a rectangle 
which corresponds to a lowpass filter with cutoff frequency f_c in the 
frequency domain you get a sinc function whose width (distance from zero 
crossing in the fourth quadrant to z.c. in the first quadrant) is 
inversely proportional to f_c. That's one of the interesting 
relationships between sinc and rectangle mediated by the Fourier 
transform (the other having to do with the area of the sinc between the 
first zero crossings and the area of the rectangle). I hope I got this 
right (avoiding any derivations on purpose because I tend to get the 
factors wrong anyway when typing into a computer), just drinking my 
morning coffee.

	Thomas