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From: analog_fever on 20 Jul 2010 18:33
I have an input signal that is generated using the following statements.

Fs = 1.4287e6 (Sampling Frequency)
Fbin = 32 (FFT Bin Number)
N = 2^17 (FFT points)
t = 0:N-1
input = A*Sin(2*pi*(Fbin/N)*t)

I send this input through a Delta Sigma modulator. And then decimate it by
100 using a CIC decimation filter. Now the question is

1. I thought that the equation I use to generate the input, should always
generate frequencies located precisely on an FFT bin. Supporting that, the
frequency of interest from the filter output after decimation looks
confined to very few bins for Fbin = 32, or multiples of it. However for
other values of Fbin, the frequency of interest is spread over a large
number of bins.

I don't understand why is the signal incoherent for other values of Fbin.
Any thoughts?
From: Greg Heath on 21 Jul 2010 02:30
On Jul 20, 6:33 pm, "analog_fever" <usu_vlsi(a)n_o_s_p_a_m.yahoo.com>
wrote:
> I have an input signal that is generated using the following statements.
>
> Fs = 1.4287e6 (Sampling Frequency)
> Fbin = 32 (FFT Bin Number)
> N = 2^17 (FFT points)
> t = 0:N-1
> input = A*Sin(2*pi*(Fbin/N)*t)
>
> I send this input through a Delta Sigma modulator. And then decimate it by
> 100 using a CIC decimation filter. Now the question is
>
> 1. I thought that the equation I use to generate the input, should always
> generate frequencies located precisely on an FFT bin. Supporting that, the
> frequency of interest from the filter output  after decimation looks
> confined to very few bins for Fbin = 32, or multiples of it. However for
> other values of Fbin, the frequency of interest is spread over a large
> number of bins.
>
> I don't understand why is the signal incoherent for other values of Fbin.
> Any thoughts?

Time:

dt = 1/Fs
T = N*dt
t = dt*(0:N-1);
t = 0:dt:T-dt;
t = linspace(0,T-dt,N);

Frequency:

df = 1/T
df = Fs/N
f = df*(0:N-1);
f = 0:df:Fs-df;
f = linspace(0,Fs-df,N);

For exact representation of sinusoid at
frequency f0 (period T0 = 1/f0) choose
an integer m such that

f0 = m*df, 1 <= m < N/2

T0 = T/m

Otherwise, leakage will occur because
of the higher frequencies caused by
the discontinuities in the periodic
extension of the waveform.

Hope this helps.

Greg
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