fir_nodelay.RdThis function is used to gather a delay-free filtering using a linear-phase (symmetric) FIR filter followed by group delay correction. Delay-free filtering is needed when the relative timing between signals is important e.g., when integrating signals that have been sampled at different rates.
fir_nodelay(x, n, fc, qual = "low", return_coefs = FALSE)
| x | The signal to be filtered. It can be multi-channel with a signal in each column, e.g., an acceleration matrix. The number of samples (i.e., the number of rows in x) must be larger than the filter length, n. |
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| n | The length of symmetric FIR filter to use in units of input samples (i.e., samples of x). The length should be at least 4/fc. A longer filter gives a steeper cut-off. |
| fc | The filter cut-off frequency relative to sampling_rate/2=1. If a single number is given, the filter is a low-pass or high-pass. If fc is a vector with two numbers, the filter is a bandpass filter with lower and upper cut-off frequencies given by fc(1) and fc(2). For a bandpass filter, n should be at least 4/fc(1) or 4/diff(fc) whichever is larger. |
| qual | An optional qualifier determining if the filter is: "low" for low-pass (the default value if fc has a single number), or "high" for high-pass. Default is "low". |
| return_coefs | Logical. Return filter coefficients instead of filtered signal? If TRUE, the function will return the FIR filter coefficients instead of the filtered signal. Default is FALSE. |
If return_coefs is FALSE (the default), fir_nodelay() returns the filtered signal (same size as x). If return_coefs is TRUE, returns the vector of filter coefficients only.
The filter is generated by a call to fir1: h <- fir1(n, fc, qual).
h is always an odd length filter even if n is even. This is needed to ensure that the filter is both symmetric and has a group delay which is an integer number of samples.
The filter has a support of n samples, i.e., it uses n samples from x to compute each sample in y.
The input samples used are those from n/2 samples before to n/2 samples after the sample number being computed. This means that samples at the start and end of the output vector y need input samples before the start of x and after the end of x. These are faked by reversing the first n/2 samples of x and concatenating them to the start of x. The same trick is used at the end of x. As a result, the first and last n/2 samples in y are untrustworthy. This initial condition problem is true for any filter but the FIR filter used here makes it easy to identify precisely which samples are unreliable.
if (FALSE) { # Make a waveform with two harmonics - one at 1/20 and another at 1/4 of the sampling rate. x <- sin(t(2 * pi * 0.05 * (1:100)) + t(cos(2 * pi * 0.25 * (1:100)))) Y <- fir_nodelay(x = x, n = 30, fc = 0.2, qual = "low") plot(c(1:length(x)), x, type = "l", col = "grey42", xlab = "index", ylab = "input x and output y" ) lines(c(1:length(Y)), Y, lwd = 2) # Returns: The input signal has the first and fifth harmonic. # Applying the low-pass filter removes most of the fifth harmonic # so the output appears as a sinewave except for the first few # samples which are affected by the filter startup transient. }