Index: Introduction to Digital Filters with Audio Applications
Introduction to Digital Filters with Audio Applications
The Simplest Lowpass Filter
Definition of the Simplest Low-Pass
Sine-Wave Analysis
A signal is typically a real-valued function of time. A discrete-time signal is typically a real-valued function of discrete time, and is therefore a time-ordered sequence of real numbers. — Click for http://ccrma.stanford.edu/~jos/filters/Definition_Signal.html
Spectrum analysis of sound is analogous to decomposing white light into its component colors by means of a prism — Click for https://ccrma.stanford.edu/~jos/mdft/Example_Applications_DFT.html
A filter in the audio signal processing context is any operation that accepts a signal as an input and produces a signal as an output. Most practical audio filters are linear and time invariant, in which case they can be characterized by their impulse response or their frequency response. — Click for https://ccrma.stanford.edu/~jos/filters/What_Filter.html
The frequency response is defined for LTI filters as the Fourier transform of the filter output signal divided by the Fourier transform of the filter input signal — Click for https://ccrma.stanford.edu/~jos/filters/Frequency_Response_I.html
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Index: Introduction to Digital Filters with Audio Applications
Introduction to Digital Filters with Audio Applications
Think of the filter expressed by Eq.(1.1) as a ``black box'' as
depicted in Fig.1.5. We want to know the effect of this black box
on the spectrum of
, where
represents the entire
input signal (see §A.1).
Figure 1.5:
``Black box'' representation of an arbitrary filter