are fundamental to digital audio processing. While we only have time here for a cursory overview of the essential features of filters, students are encouraged to pursue more advanced courses and references in filter analysis and design.
- In general, we need to manipulate our signals. Even if we only seek to measure and analyze “real world” signals, we still typically need to “process” these signals in order to compensate for measurement system “biases”.
- The processing of signals is called filtering. When applied to discrete-time signals, this processing is called digital filtering.
- Digital filters are defined by their impulse response, h[n], or the filter output given a unit sample impulse input signal. A discrete-time unit impulse signal is defined by:
- Digital filters are often best described in terms of their frequency response. That is, how is a sinusoidal signal of a given frequency affected by the filter.
- The frequency response of a filter consists of its magnitude and phase responses. The magnitude response indicates the ratio of a filtered sine wave's output amplitude to its input amplitude. The phase reponse describes the phase “offset” or time delay experienced by a sine wave passing through a filter.
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