EE5410 Signal Processing : Convolution and Filtering

EE5410 Signal Processing : Convolution and Filtering
excerpted from : Fundamentals of Digital Signal Processing
by Joyce Van de Vegte

Ch5. Convolution and filtering , page 165.

1. If a filter's impulse response is konwn, filter outputs canbe calculated using convolution.

2. Convolution is an operation that combines a filter input[x] with the filter's impulse response h[n] to produce an output y[n]. It is described by the equation

y[n] = x[n]*h[n]

but is computed most easily using a graphical or tabular method.

3. In convolution, an impulse response sequence sequence inches past an input sequence, and an outputed is calculated at EACH step. Boundary effects occurs whenever the input sequence fails to encompass the impulse response sequence completely.

For FIR filters, boundaryeffects have a well- defined end. For IIR filters, boundary effects NEVER truly disappear, but do become small.

4. The initial output samples, which are significantly influences by boundary effects, form the transient part ceases. For a constant input, the steady state output will be constant. for a sinusoidal input, the steady state output will be sinusoidal.

5. A difference equation can be reexpressed as a convolution, and vice versa.

6. A moving average filter smoothes a signal by producing a running average of its sample values.

7. The two-dimensional version of an impulse response is a convolution kernel. The convolution kernel is convolved with a digital image to produce a filter image.

8. A low pass convolution kernel BLURS an image by averaging gray scale levels over neighborhoods of pixels.