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DSP: What do you mean by the Filter Lenght?

  1. Dec 10, 2009 #1
    What does the length of the filter in DSP means?

    What does it refer physical or practical when it states that "signal transmission path models have long impulse response?"

    And why do audio signal transmission paths have long impulse response?
  2. jcsd
  3. Dec 11, 2009 #2


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    Staff: Mentor

    Welcome to the PF. What is your background in DSP so far? Self study, or have you taken an intro class yet? They are very useful building blocks to be familiar with!


    Where are you in school right now?
  4. Dec 11, 2009 #3
    I am going on with self study sir.
  5. Dec 11, 2009 #4


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    Staff: Mentor

    Fair enough, but we will still follow the PF guidelines for schoolwork and self-study. Which means that we can offer some tutorial hints, but we expect you to do the bulk of the research and work.

    So what learning resources do you have available for your study of DSP? There are quite a few on the web. Have you studied analog filters before, and are now learning about DSP, or is your study of digital filters your first intro to filters overall?

    In filter design, we speak of different polynomials that can be used, to give us different advantages and disadvantages in our filter designs. Are you familiar with the different polynomial classes, and what they are used for?

    And a hint (or motivator for your further study on the subject) -- what would the filter length have to do with the passband ripple on a Chebychev polynomial digital filter...?
  6. Dec 11, 2009 #5
    I too wish the same. I am searching online and i am posting the things that i can not find there.

    I am doing my engineering in INDIA. here the study methodology and the standard are not much high. The staffs are focusing only on academics and mark scoring. They are not much helping in research areas, and not even well versed in these areas. So i am mostly relied on some books and online resource.

    I have a outer overview and understanding on filters, but not into much depth.


    I have studied and solved problems in cheby, butterworth etc, but without much understanding of actual concept in it. Sorry for this, and my educational system is luike that. Much worried for this.

    I will search for and try to learn about this.
  7. Dec 11, 2009 #6


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    Staff: Mentor

    Good start. Let us know what you find.
  8. Dec 11, 2009 #7

    Sounds like your refering to what's called a finite response filter or FIR. It takes in samples and passes those signals along (in a digital format) like a shift register (if your a digital guy) or a bucket brigade (for old analog guys ;).

    The newest sample is always coming in one side of the sequence, while the oldest one is going to bit heaven. The number of samples being held, altogether, is refered to as the number of taps or filter length.

    Now, comes the stranger part - why they call it taps. Essentially, you can make a great many different responses with this filter - some that seem almost impossible.

    To do this your neighbourhood underpaid mathmatician (or over paid engineer with software) comes up with a table of values. There's one value for each "tap" (stored sample). Each time a new sample comes in, the DSP runs through every stored sample, multiplies it with the corresponding value from the table, and adds up the sum of all those multiplications. The total of all that addition is the output of the filter.

    Having to multiplying every single sample and add it is a lot of work, considering the DSP must do so every single time a new sample comes in. So DSP are designed to be able both multiple and add in the same instruction. Also, they can do this to long strings of numbers (like all the samples you're holding) without having to be told over and over. Essentially they're told where to get it, how many to do, and chip will multiply and add till the sequence is done.

    Now, as to the impulse response. If you have only one sample that has a value and all of the rest are zero, then that one sample would be an impulse. For an FIR filter, you would expect that impulse to come out looking different at different times depending on how far it's shifted through the taps and what the corresponding table value looks like. In any case, you know that once the impulse has shifted to the end of the filter, it's gone. Hence the expression "Finite" Impulse Response.

    Some filters feed part of their output back into an earlier stage of the filter. Hence theoretically, an impulse will never altogether reach zero. It will keep getting smaller, but there's always a peice that's left over and it goes back in. Such filters are refered to as Infinite Impulse Response (IIR) filters. To me, these remind me more of my treasured analog filters, though of course you still have to go through some math to get one to work - sigh...

    Well, as to application. The FIR filters are great. Not great. WONDERFUL, at communications processing. They have a lot of delay, going through all those taps, but they can filter a mesquito buzz out of a car crash. They can be updated in real time for noise cancelation and echo reduction. They're just good and wholesome. AND, if you know what you're doing they're not all that difficult to design.

    As to IIR filters, well... They have a place. I like em as resonators and "digital" oscillators, and they're pretty good for lead-lag networks in control systems. FIR's have that whole thing with process delay, so generally they're not considered good stuff for closed loop control.

    Well, I hope this helps a bit. I do ramble on at times...

    Best Wishes and good luck on your work,

  9. Dec 13, 2009 #8
    This made me clear mike. thanks a lot.
  10. Dec 22, 2009 #9
    An FIR filter for example H(z)= 1+h(0)/z + h(1)/z*z + h(2)/z*z*z, has length 4 and order 3.
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