sweeptone

R2026b

Exponential swept sine

The sweeptone function has changed. For more information, see Version History.

Syntax

excitation = sweeptone()

excitation = sweeptone(swDur)

excitation = sweeptone(swDur,silDur)

excitation = sweeptone(swDur,silDur,fs)

excitation = sweeptone(___,Name=Value)

Description

excitation = sweeptone() returns an excitation signal generated using the Exponential Swept Sine (ESS) technique. By default, the signal has a 6.157-second duration, followed by 4 seconds of silence, for a sample rate of 44.1 kHz.

excitation = sweeptone(swDur) specifies the target duration of the ESS signal.

excitation = sweeptone(swDur,silDur) also specifies the duration of the silence following the ESS signal.

excitation = sweeptone(swDur,silDur,fs) also specifies the sample rate of the sweep tone as fs in Hz.

excitation = sweeptone(___,Name=Value) specifies additional options using one or more name-value arguments for any of the previous syntaxes. Options include the excitation level and the range of sweep frequency.

Examples

Generate ESS Signal with Default Parameters

Since R2026b

Generate a 6.157-second exponential swept sine (ESS) signal at a rate of 44.1 kHz. The sweep goes from 10 Hz to 22 kHz, followed by with a 4-second silence.

exc = sweeptone();

Visualize the excitation in time. The excitation level of –6 dB yields an amplitude of ${10}^{-6/20}=0.5012$V.

t = (0:numel(exc)-1)/44100;
plot(t,exc)
xlabel("Time (s)")

Generate ESS Signal with Sample Rate

Generate an exponential swept sine (ESS) signal sampled at a rate of 48 kHz. The sweep lasts for approximately 3 seconds and follows with a 2-second silence.

fs = 48e3;
exc = sweeptone(3,2,fs);

Visualize the excitation in the time-frequency domain. The default frequency sweep goes from 10 Hz to 22 kHz.

spectrogram(exc,512,0,1024,fs,"yaxis")

Estimate Impulse Response Using Sweep Tone Excitation

Create a sweep tone excitation signal with a sweep that goes from 20 Hz to 20 kHz for approximately 2 seconds and ends with a 1-second silence. Specify the sample rate as 44.1 kHz.

exc = sweeptone(2,1,44100,SweepFrequencyRange=[20 20e3]);

plot((0:numel(exc)-1)/44100,exc)
title("Excitation")
xlabel("Time (seconds)")

Pass the excitation signal through an infinite impulse response (IIR) filter and add noise to model a real-world recording (system response).

[B,A] = butter(10,[0.1 0.7],"ctf");
rec = ctffilt(B,A,exc);
nrec = rec + 0.12*randn(size(rec));

plot((0:numel(nrec)-1)/44100,nrec)
title("System Response")
xlabel("Time (seconds)")

Pass the excitation signal and the system response to the impzest function to estimate the impulse response. Truncate the estimate to 100 points. Use impz to determine the true impulse response of the system. Plot the true impulse response and the estimated impulse response for comparison.

irEstimate = impzest(exc,nrec);
irEstimate = irEstimate(1:101);

irTrue = impz(B,A,101);
plot(0:100,irEstimate,"-",0:100,irTrue,"--")

legend(["True" "Estimated"] + " impulse response")
xlabel("Sample Number")

Input Arguments

swDur — Target duration of ESS signal (in seconds)

6 (default) | scalar in the range [0.5, 60]

Target duration of the ESS signal (in seconds), specified as a scalar in the range [0.5, 60].

The actual duration, T, depends on swDur, the sample rate fs, and the range of sweep frequency specified as SweepFrequencyRange = [f1 f2]. The function adjusts the duration to ensure a synchronized phase of 0 radians at both ends of the ESS signal. This code calculates T:

T =  round(swDur*f1/log(f2/f1))/(f1/log(f2/f1))

The maximum difference between T and swDur is 0.5/(f1/log(f2/f1)) seconds.

Data Types: single | double

silDur — Duration of silence after ESS signal (in seconds)

4 (default) | positive scalar

Duration of silence after ESS (in seconds), specified as a positive scalar.

fs — Sample rate (in Hz)

44100 (default) | positive scalar

Sample rate (in Hz), specified as a positive scalar.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: sweeptone(3,2,48e3,ExcitationLevel=-5)

ExcitationLevel — Level of excitation signal to generate (in dB)

-6 (default) | scalar in the range [–42, 0]

Level of the excitation signal to generate (in dB), specified as a scalar in the range [–42, 0].

When you specify ExcitationLevel=a, the function scales the ESS signal by 10^(a/20) before returning excitation.

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

SweepFrequencyRange — Range of sweep frequency (Hz)

[10 22000] | two-element positive-valued row vector

Range of sweep frequency in Hz, specified as a two-element positive-valued row vector. Each value must be unique.

• You can specify the sweep frequency range as low to high or high to low. For example, [10 22000] and [22000 10] are both valid inputs.

• The largest value of the sweep frequency range must be less than or equal to fs/2.

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

Output Arguments

excitation — Excitation signal

column vector

Excitation signal generated using the ESS technique, returned as a column vector. The length of the column vector is about (swDur+silDur)*fs samples.

Data Types: single | double

More About

Exponential Swept Sine (ESS)

The ESS signal is a logarithmic swept-frequency sinusoidal waveform that is useful for harmonic frequency response analysis and nonlinear characterization of audio systems.

Assume an ESS signal s that depends on these parameters:

• T₀ — Target duration, in seconds

• f₁ — Minimum frequency of the frequency sweep, in hertz

• f₂ — Maximum frequency of the frequency sweep, in hertz

• f_s — Sample rate, in hertz

• a — Excitation level, in decibels

To ensure a synchronized phase at the start and end of the ESS signal, the actual duration of the ESS signal, T, differs slightly from T₀, so that

$$T=\text{round}\left(T_0\frac{f_1}{\ln (f_2/f_1)}\right)\frac{\ln (f_2/f_1)}{f_1}=L\ln (f_2/f_1)$$.

Then, s is:

s = 10^a/20 sin(2πf₁Le^t/L)

To reduce the spectral leakage caused by transients at very low and very high frequencies, the sweeptone function fades both ends of s before appending silence.

• The function applies fading using the left half of a Kaiser-Bessel-derived window with 2N points and a tuning parameter β = 5, where N is the number of samples spanning the fade-in and fade-out durations.

• The fade-in duration, t_fade-in, is defined as $$t_{\text{fade-in}}=\min \left(\frac{0.25}{\ln (\max (5,f_1))},\frac{T}{10}\right)$$.

• The fade-out duration, t_fade-out, is defined as $$t_{\text{fade-out}}=\min \left(\frac{0.05}{\ln (\max (5,f_2))},\frac{T}{10}\right)$$.

References

[1] Farina, A. "Advancements in Impulse Response Measurements by Sine Sweeps." Presented at the Audio Engineering Society 122nd Convention, Vienna, Austria, 2007.

[2] Novák, A., Simon, L, Kadlec, F., and Lotton, P. "Nonlinear System Identification Using Exponential Swept-Sine Signal." IEEE Transactions on Instrumentation and Measurement, Vol. 59, No. 8, pp. 2220-2229, 2009.

Extended Capabilities

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

Version History

Introduced in R2018b

R2026b: Updated implementation to support harmonic frequency response analysis

The sweeptone function supports harmonic frequency response analysis.

• The swDur argument no longer specifies the exact duration of the ESS signal. Instead, this argument specifies a target duration. The function uses this argument to determine the actual duration of the generated ESS signal, which differs slightly to ensure a synchronized phase at both ends.

• The fading applied to both ends uses a Kaiser-Bessel-derived window instead of a sine window. The fade-in and fade-out durations depend on the range of the frequency sweep and on the actual duration of the generated ESS signal.

R2022b: Exponential swept sine supports longer duration

The duration of the ESS signal, specified by the swDur argument, can be a maximum of 60 seconds. Previously, the combination of the ESS signal duration and the duration of the following silence could not exceed 15 seconds.