Re: How does sampling frequency affects a digital filter ?


mel wrote:
Hello,

I am writing a digital filter but it seems that according to
the sampling frequency my filter should change ... how does this
happens ? being a digital filter there is no such a thing as sampling
frequency, right ?

Interesting question! I am not sure it is what you mean, but I
interpret it as "If the signal is specified in discrete-time domain,
the signal is never sampled and there is no such thing as a sampling
frequency." I agree, this is a valid question.

One more thing ... it seems that the cut off frequency should
affect my filter too ... the cut off frequency is the bandwidth of the
transmitting channel, right ? How should it affect the filter ?

The key here is that the filter in frequency domain is specified in
terms of "normalized frequencies." If we agree to use "time" as
name for the running variable in signal domain, and "fequency"
in Fourier domain (we could have used space and wavenumber,
or something else), the discrete-time signal has a limited-width
spectrum. To make sense of it all, and relate it to the more intuitive
case of a sampled signal, we speak of a "normalized sampling
frequency" with sampling period 1. If we do that, all the T factors
in the forward and inverse Fourier transforms disappear, and we
still can speak a comprehensible language.

In that case, the filter cut-off frequency is still well-defined,
relative
to the normalized sampling frequency.

f_c = F_c/F_s = f_c*T/(f_s*T) = f_c*1/1*1 = f_c.

In fact, most filter design packages work in this normalized domain,
introfducing the T factor only when needed.

Sorry if these questions sounds dumb,

No, they certainly are not. These are the kinds of questions that
either make you shy DSP as a dicipline, or make you gain insight.

Rune

.

Relevant Pages

  • Re: The Difference Betweeen 96khz & 192khz
    ... > If you digitize with a sampling rate of 48000, ... > to use a filter which stops all frequencies above ... 192,000 Hz sound any different doing a good job of sampling ... upper sample rate to 192,000 is probably not going to sound ...
    (rec.audio.pro)
  • Re: Envelope Detector using Hilbert Transform
    ... >>> I have working with ultrasound signals from a solid state ... >>> Khz) are digitized through a sampling card and imported into MATLAB, ... >>> implementing it in real time on the DSP processor. ... >>fit for the filter to make the passband ripple small. ...
    (comp.dsp)
  • Re: Digital processing of analog TV broadcast
    ... FPGA clock - fixed and stable. ... I regenerate the chroma subcarrier using a numerically controlled ... numerically controlled oscillator, and low-pass filter. ... carefully plotting out the sampling components and their aliases. ...
    (sci.electronics.design)
  • Re: Comparing matched and Wiener filters
    ... "filter across all time and sample" viewpoint of matched-filtering, ... the output for the sampling points (i.e. correlation, ... You are interested in comparing MF vs Wiener, ... MF does not maximize SNR in the ...
    (comp.dsp)
  • Re: Projective warping of an Image
    ... How are you doing the sampling? ... you need to use the highest quality resampling method you ... Note that when doing projective warping, some parts of the output image ... it's just acting as a reconstruction filter. ...
    (sci.image.processing)
Loading