sgolay (Signal Processing Toolbox)

Savitzky-Golay filter design.

Syntax

b = sgolay(k,f)
b = sgolay(k,f,w)

Description

b = sgolay(k,f)

designs a Savitzky-Golay FIR smoothing filter b. The polynomial order k must be less than the frame size, f, which must be odd. If k = f-1, the designed filter produces no smoothing. The output, b, is an f-by-f matrix whose rows represent the time-varying FIR filter coefficients. In a smoothing filter implementation (for example, sgolayfilt), the last (f-1)/2 rows (each an FIR filter) are applied to the signal during the startup transient, and the first (f-1)/2 rows are applied to the signal during the terminal transient. The center row is applied to the signal in the steady state.

b = sgolay(k,f,w)

specifies a weighting vector w with length f, which contains the real, positive-valued weights to be used during the least-squares minimization.

Remarks

Savitzky-Golay smoothing filters (also called digital smoothing polynomial filters or least squares smoothing filters) are typically used to "smooth out" a noisy signal whose frequency span (without noise) is large. In this type of application, Savitzky-Golay smoothing filters perform much better than standard averaging FIR filters, which tend to filter out a significant portion of the signal's high frequency content along with the noise. Although Savitzky-Golay filters are more effective at preserving the pertinent high frequency components of the signal, they are less successful than standard averaging FIR filters at rejecting noise.

Savitzky-Golay filters are optimal in the sense that they minimize the least-squares error in fitting a polynomial to each frame of noisy data.

`fir1`	Window-based finite impulse response filter design - standard response.
`firls`	Least square linear-phase FIR filter design.
`filter`	Filter data with a recursive (IIR) or nonrecursive (FIR) filter.
`sgolayfilt`	Savitzky-Golay filtering.