upfirdn

Upsample, apply FIR filter, and downsample

Syntax

y = upfirdn(x,h)

y = upfirdn(x,h,p)

y = upfirdn(x,h,p,q)

Description

y = upfirdn(x,h) filters the input signal x using an FIR filter with impulse response h. No upsampling or downsampling is implemented with this syntax.

y = upfirdn(x,h,p) specifies the integer upsampling factor p.

y = upfirdn(x,h,p,q) specifies the integer downsampling factor q.

Examples

Filter and Upsample Linear Chirp

Since R2026a

Design a 50th-order FIR lowpass filter to suppress imaging artifacts from upsampling. The upsample factor is 5. Compute the group delay and impulse response of the filter.

p = 5;

n = 50;
h = p*fir1(n,1/p);
dl = grpdelay(h,1,1);
freqz(h)

Define a linearly swept cosine (chirp) signal for one second at a sample rate of 30 Hz.

Fs = 1e3;
t = single(0:1/Fs:1)';
x = chirp(t,20,t(end),150);

Filter and upsample the chirp signal. Since the input signal has single precision, the output also has single precision.

xu = upfirdn(x,h,p);

Compare the input and output signals. Compensate for the delay introduced by the filter. Generate the corresponding resampled time vector.

xu = xu(dl+1:end);
tu = single(0:(length(xu)-1))/(Fs*p);
plot(t,x,".-",MarkerSize=10)
hold on
plot(tu,xu,".-",MarkerSize=4)
hold off
xlim([0 0.5])
xlabel("Time (s)")
legend(["x" "xu"])

Convert from DAT Rate to CD Sample Rate

Change the sample rate of a signal by a rational conversion factor from the DAT rate of 48 kHz to the CD sample rate of 44.1 kHz. Use the rat function to find the numerator L and the denominator M of the rational factor.

Fdat = 48e3;
Fcd = 44.1e3;
[p,q] = rat(Fcd/Fdat)

p = 
147

q = 
160

Generate a 1.5 kHz sinusoid sampled at $f_{\text{DAT}}$ for 0.25 seconds. Plot the first millisecond of the signal.

t = 0:1/Fdat:0.25-1/Fdat;
x = sin(2*pi*1.5e3*t);
stem(t,x)
xlim([0 0.001])
xlabel("Time (s)")
hold on

Design an antialiasing lowpass filter using a Kaiser window. Set the filter band edges as 90% and 110% of the cutoff frequency, $\left(f_{\text{DAT}}/2\right)\times \min \left(1/L,1/M\right)$. Specify a passband ripple of 5 dB and a stopband attenuation of 40 dB. Set the passband gain to L.

f = (Fdat/2)*min(1/p,1/q);
d = designfilt("lowpassfir", ...
    PassbandFrequency=0.9*f,StopbandFrequency=1.1*f, ...
    PassbandRipple=5,StopbandAttenuation=40, ...
    DesignMethod="kaiserwin",SampleRate=48e3);
h = p*tf(d);

Use upfirdn with the filter h to resample the sinusoid. Compute and compensate for the delay introduced by the filter. Generate the corresponding resampled time vector.

y = upfirdn(x,h,p,q);

delay = floor(((filtord(d)-1)/2-(p-1))/p);
y = y(delay+1:end);
t_res = (0:(length(y)-1))/Fcd;

Overlay the resampled signal on the plot.

stem(t_res,y,"*")
legend("Original","Resampled",Location="southeast")
hold off

Input Arguments

x — Input signal

vector | matrix

Input signal, specified as a vector or matrix. If x is a vector, then it represents a single signal. If x is a matrix, then each column is filtered independently. For more details, see Tips.

Data Types: single | double

h — Filter impulse response

vector | matrix

Filter impulse response, specified as a vector or matrix. If h is a vector, then it represents one FIR filter. If h is a matrix, then each column is a separate FIR impulse response sequence. For more details, see Tips.

Data Types: single | double

p — Upsampling factor

1 (default) | positive integer

Upsampling factor, specified as a positive integer.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

q — Downsampling factor

1 (default) | positive integer

Downsampling factor, specified as a positive integer.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

y — Output signal

vector | matrix

Output signal, returned as a vector or matrix. Each column of y has length ceil(((length(x)-1)*p+length(h))/q).

If you specify x or h as type single, then upfirdn performs the filtering operation using single-precision arithmetic, and returns y in single precision. Otherwise, upfirdn returns y as type double.

Note

Since upfirdn performs convolution and rate changing, the output signals y have a different length than the input signals x. The number of rows of y is approximately p/q times the number of rows of x.

Tips

The valid combinations of the sizes of x and h are:

1. x is a vector and h is a vector.

   The inputs are one filter and one signal, so the function convolves x with h. The output signal y is a row vector if x is a row vector; otherwise, y is a column vector.

2. x is a matrix and h is a vector.

   The inputs are one filter and many signals, so the function convolves h with each column of x. The resulting y is a matrix with the same number of columns as x.

3. x is a vector and h is a matrix.

   The inputs are multiple filters and one signal, so the function convolves each column of h with x. The resulting y is a matrix with the same number of columns as h.

4. x is a matrix and h is a matrix, both with the same number of columns.

   The inputs are multiple filters and multiple signals, so the function convolves corresponding columns of x and h. The resulting y is a matrix with the same number of columns as x and h.

Algorithms

upfirdn uses a polyphase interpolation structure. The number of multiply-add operations in the polyphase structure is approximately (L_hL_x – pL_x)/q where L_h and L_x are the lengths of h(n) and x(n), respectively. For long signals, this formula is often exact.

upfirdn performs a cascade of three operations:

1. Upsample the input data in the matrix x by a factor of the integer p (inserting zeros)

2. FIR filter the upsampled signal data with the impulse response sequence given in the vector or matrix h

3. Downsample the result by a factor of the integer q (throwing away samples)

The FIR filter is usually a lowpass filter, which you must design using another function such as firpm or fir1.

Note

The function resample performs an FIR design using firls, followed by rate changing implemented with upfirdn.

References

[1] Crochiere, R. E. "A General Program to Perform Sampling Rate Conversion of Data by Rational Ratios." Programs for Digital Signal Processing (Digital Signal Processing Committee of the IEEE Acoustics, Speech, and Signal Processing Society, eds.). New York: IEEE Press, 1979, Programs 8.2-1–8.2-7.

[2] Crochiere, R. E., and Lawrence R. Rabiner. Multirate Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1983.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a

R2023a: Use single-precision data

The upfirdn function supports single-precision data.