Filter Design questions...

[EdRyan]

Another programming related question. This time using Mathworks matlab..

I need to design the following FIR Filter

16K sample rate
3.625K cutoff, as a low pass

Best design using 60 taps (not including kaiser window)

The problem I'm having is specifying the transition width at the edge of the passband. I know its related to the sample rate, but can't remember exactly what it is. I've tried googling it and I just get a lot of stuff I don't need !
I'm also stuck on how you write the ideal low pass function equation as a piece of code...
And why specify the filter length (60) without including the window. Whats going on here ?

I realise it might be a bit too geeky here, but thought it might be worth a shot with people like Khazul, stagesound etc..

[Khazul]

Been a while since I mess with filters and I usually went for simpler reproductions of analog filter behaviour which you can hack up using basic integration techniques

Out of curiosity, whats your application for this - as this sounds quite steep?

[EdRyan]

This is a piece of coursework.

I struggle with the maths side of it lol.

[Khazul]

Ah OK... then you probably know way more than me - it not something the was available for study when I was young

As a guess from what little I know of some DSP theory - I think FIR filters are based upon calculating taps in the frequency domain - the more taps, the greater the accuracy of the filter response to a desired filter response. I think the window function effectly tells you the response for each tap.

Thinking about it - I dont get the thing about specifying the number of taps *not* including those within the window as I thought you basically only had to calculate (as a minumum) the taps within the window function - as anything outside is a zero and so can be omitted from some of the calculations - either yielding effectively a tend to zero or a tend to unity gain outide the window - depending on the filter repsonse type?

Within the window - I think more taps = more accurate fitting of the frequency repsonse curve to a desired frequency reponse - then the question becomes whats the definition of a 'best' design for the given application.

[EdRyan]

You are partly correct there dude.

The ideal transfer function of a filter is defined as an IIR and analogous process. As a result of that, it would have infinite + or - values. That means the filter couldn't be realised as a digital FIR.

The window function effectively transforms the ideal IIR function into a FIR by specifying N (tap) points. The easiest way of describing it is that it samples the shape of the filter. therefore, the more samples. the more accurate the digital version will be. There are other important factors associated with this. Things like ripple in the passband and rate of attenuation are also linked to the number of taps.

Alto, the moer taps you have, the more coeffecients you generate (I think)...and so he more demanding the filter is. Like you say, 'best' is just another word for comprimise.

I'm gonna email my tutor now and ask him about deltaf (passband width) and why he spec'd the taps without the window. It's a bit cryptic. Everyone else's either tells you straight which window to use, or specifies passband/ripple/attenuation functions that are more then a clue as to which window to use.. I jsut feel Im missing some info.

[EdRyan]

sorted.

I was correct, it needed to be either 59 or 61 taps, to keep the filter order even. Essentially, the value of 0 has to be the extra 1. So that if you divide 61/2 ( to cover negative and positve ranges)..you get 30 taps in either direction, with the remaining 1 being used as 0.
Also found out the dsp board we're running on can't run at sample rates lower then 48k.

And his just meant to say not to use the kaiser window, use an alternative (I picked the blackman as its the next best overall).

Calculating the transition width turns out to be easy. The width of the blackman transition band is 5.5/N. So it's normalised value is 5.5/60. You can then go one step 'backwards' with equations and calculate the non normal transfer required.

And so, I present to you lot. My linear phase low pass filter



I've jsut gotta write the program to derive the co-effs, and then load them onto the dsp codec...and I will have my first working dsp hardware routine