Filtering by Convolution

Discussion in 'Wireless & RF Design' started by idmond, Jan 5, 2013.

  1. idmond

    Thread Starter Member

    Oct 5, 2010
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    we used to study, back in college, how to do analog filtering of signals
    by convolving the analog filter impulse response with the input signal.
    That was the theory, right?

    I know we can easily do this for digital filters, but I'm kind curious about this, can we still do it, in practice, for analog filters
    with analog integrators like op-amps?

    and if it is not possible, Why?
     
    Last edited: Jan 5, 2013
  2. MrChips

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    Oct 2, 2009
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    This is correct as a low pass filter.
    Feeding the signal into a capacitor smooths out the fluctuations and removes high frequencies. This is an integrator.
    Convolution performs signal averaging and accommplishes the same thing.
     
  3. idmond

    Thread Starter Member

    Oct 5, 2010
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    yes, i know that a low pass filters is actually an integrator.
    but i meant that: is it possible to take the impulse response of a low pass filter for instance,
    then build an equivalent analog hardware that does the same function of a low pass filter, but now using the method of convolution;
    i.e the hardware in mind should delay the impulse response and multiply it with the input signal then integrate, all of this in continuous time. that's my point.
     
  4. WBahn

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    Mar 31, 2012
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    If you build a linear analog circuit that has a particular impulse response, the it will, by nature, convolve the input signal with the filter's impulse response to produce the output. Convolution is simply a mathematical description of the physical processing that occurs in the circuit.
     
  5. idmond

    Thread Starter Member

    Oct 5, 2010
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    yeah, I know that the output of a linear circuit (whether it's a filter or any signal conditioning circuit) is just a result of the circuit doing convolution with its impulse response, and that's how i get the output.

    but i want to convince myself with an experiment, that i can predict the output of a linear analog circuit (say, a filter) by doing convolution with the circuit impulse response, i mean just like how they filter things in the digital domain, they take impulse response of an analog filter that has the frequency response they want then sample it and convolve it with the samples of the input signal, and they get at the output of the filter the same signal that they would have got if they applied the same input signal to the input of the corresponding analog filter. Now, all i want is to do the same thing in the analog domain with analog circuit(filter). is it possible?

    I don't want the analog filter, by nature and inherently, to do the filtering by convolution. I want to do the filtering by doing convolution experimentally with analog circuit, just like how they do it with digital filter.

    I hope you understand what I'm trying to say here.
     
  6. MrChips

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    Oct 2, 2009
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    Maybe we do but it doesn't make sense.
    As WBahn says, convolution in digital filtering is a mathematical operation in the digital domain.
    In the real world, convolution just happens automatically. You don't do convolution explicitly. It happens implicitly when the signal is transformed by the filter.
     
  7. idmond

    Thread Starter Member

    Oct 5, 2010
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    since it's a mathematical operation, why can't we do it in the analog domain like we we do it in the digital domain. we have multipliers, integrators in the analog domain analogous to multipliers and adders in the digital domain.

    we do it explicitly and intentionally in the digital domain, right?
    so why we can we do it explicitly in the digital domain but not in the analog domain?
     
  8. WBahn

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    Mar 31, 2012
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    What you are asking to do is like saying you want to experimentally verify in the analog domain that the voltage across a resistor is the product of its resistance and the current through it. But you don't want to use the fact that this is the natural behavior of a resistor, instead you want to build an analog circuit that explicitly does this.

    To perform convolution in the analog world, I guess you could take your input signal and rapidly sample it into N of different distinct signals that, summed together, approximate the input signal. Then apply those signals to N different copies of the analog filter and sum up the outputs of the N filters to produce you final output signal.
     
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  9. MrChips

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    Oct 2, 2009
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    I was looking for analogies to demonstrate why it doesn't make sense to demonstrate convolution in the analog domain.

    The only thing I can think of is to say a vibrating molecule has temperature, but wanting to demonstrate temperature by separating the molecule from its vibrational behaviour.

    Or perhaps light beams enter a convex lens and form an image on a screen. The light beam is convolved with the transfer function of the lens and is transformed into a real image. It would be very difficult to demonstrate this convolution using the digital process.
     
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