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Digital Signal Theory
Digital Filters
29
Computer Science
Graduate
05/09/2012

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Term
Causal Filter
Definition
The output depends on any current, past, or future input. (EQ, reverb, delay, etc.)
Term
Non-Causal Filter
Definition
The output is not dependent on any current, past, or future input (pre-delay)
Term
Linear Time Invariant Filter (LTI)
Definition
A digital filter where there is no harmonic distortion clipping, no intermodulation distortion, both linear and time invariant, is causal.
Term
Reverb
Definition
LTI filter, both linear and time-invariant.
Term
EQ
Definition
LTI filter
Term
Compressor
Definition
Time invariant filter.
Term
Impulse
Definition
A time domain signal that has as high of an amplitude as possible at 0, but has zero amplitude. Characterized by a loud, short sound. The shorter the signal, the wider the spectrum & vice versa.
Term
Impulse Response
Definition
The response to an impulse, that contains all frequencies in an response at equal amplitudes. Works in the time domain.
Term
Convolution
Definition
The sum of every sample of the input signal, multiplied by the sum of every sample of the impulse, added together, produces a convolved signal.

-Convolved signals will be either scaled or delayed

-The output of the convolved signal should be N+M-1, where the length of output signal is one sample shorter than the sum of the lengths of the two convolved signals put together.
Term
The law of convolution
Definition
Convolution in the time domain is equal to multiplication in the frequency domain.
Term
Fast Convolution
Definition
1) Two signals are convolved together in the time domain
2) An FFT occurs to bring the two signals into the frequency domain
3) They are multiplied together; essentially convolving them
4) An IFFT occurs to bring the convolved signal back into the time domain.
Term
Feed Forward Filter
Definition
A simple delay, which is added together towards the output Z-^1

*Multiplied by x[n]
Term
Feedback Filter
Definition
Coefficients are subtracted together from the output.

*Multiplied by y[n]
Term
Digital Filter Equation
Definition
Noncausal, LTI, Direct Form II

y[n] = [the sum of all feed forward] coefficients] x[n-i] - [the sum of all feedback coefficients] y [n-j]
Term
Finite Impulse Response Filter (FIR)
Definition
A feedforward only filter.
Term
Infinite Impulse Response Filter (IIR)
Definition
A feeback filter, that is potentially unstable.
Term
Filter Order
Definition
1st order = y[n] = x[n] + x[n-1]

2nd order = y[n] = 0.5x[n] - 0.5
Term
Impulse Response Equation
Definition
x = [1 0 0 0 0 0 0 0 0 0]
Term
Steady State Filter Response
Definition
A stable input will produce a consistent output.
Term
Unstable Filter Response
Definition
an infinite impulse will produce and unstable, infinite response. IIR Filter.
Term
Transient Time (Decay TIme)
Definition
The T60 of an impulse for an IIR Filter. The filter order divided by the sample rate for a FIR Filter.
Term
Bandwidth of a Filter
Definition
The distance from peak to peak.
Term
Center Frequency (fcenter, Q), Resonant Frequency
Definition
One frequency is accentuated, while all others are sharply cutoff; determines the type of filter.
Term
Measuring the bandwidth of a filter
Definition
fcenter / bandwidth

Higher bandwidth = the smaller the center frequency will be, producing a duller filter.

Lower bandwidth = higher center frequency and a sharper filter.
Term
Bi-quad filter
Definition
Quadratic Equation / Quadratic Equation
Term
Comb filter
Definition
All frequencies are cancelled out at evenly spaced frequencies.

[1 0 0 0 0 0 0 0 0 0 0] = evenly spaced frequencies, close together [1 0 0 0] = widely spaced apart frequencies
Term
IIR Comb Filter
Definition
Sharp resonant peaks
Term
Poles
Definition
Feedback coefficients
Term
Zeros
Definition
Feedforward coefficents
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