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Digital bandwidth clarification

Discussion in 'General Electronics Discussion' started by max_torch, Dec 8, 2014.

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  1. max_torch

    max_torch

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    1
    Feb 9, 2014
    I know that bandwidth capacity of a channel/medium is the difference between the highest and lowest frequencies that can be sent across that channel, and I get this when it comes to sending analog signals that have varying frequency, like if you say a low sounding note that has a low frequency and if you say a high pitch note that has a high sounding frequency. But what I don't get is how bandwidth works with regards to digital signals. When would the signal have a low freq and when would it have a high freq? Also here is a diagram: band.png
    Because I don't understand bandwidth and frequencies in a digital signal, I don't understand what causes the bandwidth dependencies in the third row. I don't understand how the width or rise time and fall time of a pulse could determine a frequency in the signal.
     
  2. Harald Kapp

    Harald Kapp Moderator Moderator

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    2,153
    Nov 17, 2011
    A digital signal can be represented as the sum of sine waves of different frequency, phase and amplitude. This is called a Fourier series.

    In theory the bandwidth of a digital signal is infinite as one can mathematically find non-zero coefficients for any arbitrarily high frequency as part of the digital signal's spectrum.

    In practice the influence of frequency components sinks with rising frequency, meaning that higher frequency components have a negligible effect on the digital signal's waveform. It is up to the designer of e.g. a transmission channel to decide which components need to be transmitted and which can be cut off. This effectively defines the bandwidth of the channel.

    In your example the main factor influencing the required bandwidth to reproduce or transmit the signal with a given degree of fidelity is liste in the bottom row (3). When doing the matahmatical analysis for a Fourier series it is this factor that has a strong influence on the values of the coefficients for higher frequencies.

    A simple example to illustrate the concept of bandwidth in digital signals: Apply a square wave to an RC low-pass filter. Vary the cutoff-frequency of the filter with respect to the fundamental frequency of the square wave and observe the output of the filter. You can easily do this on a breadboard on in a simulator.
     
  3. max_torch

    max_torch

    106
    1
    Feb 9, 2014
    What about if I use a fourier transform to convert the digital signal from a function of time into a fucntion of frequency, will that also make it obvious? By the way I have no idea yet how to do a Fourier transform but if it will make it clear then I will look it up.
     
  4. Harald Kapp

    Harald Kapp Moderator Moderator

    10,079
    2,153
    Nov 17, 2011
    A Fourier series is but a special case of a Fourier transform (discrete time Fourier transform).
    The main difference is that a Fourier transform is continuous, whereas a Fourier series is discrete with respect to frequency.
     
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