The Impulse approach to measuring frequency response suffers from the low energy delivered to the system because the pulse is so narrow, often necessitating the averaging of many responses to bring the desired signal out of the system noise floor.

The Step response approach relies upon some mathematical trickery: The derivative of a step function is an impulse function, so it is perfectly "legal" to apply a step to the system and then take the derivative of the response to get the impulse response, and hence the frequency response. But a step has considerably more energy than a narrow pulse, so the response is much larger.

There's more trickery: Applying a derivative to the waveform is equivalent to tilting the spectrum upward at +6 dB per octave. In Y-log Spectrum mode that can be done easily with the Tilt option in the Spectrum Curves dialog. This is a way to get an impulse response with less noise, or with little or no response averaging.

To create the step signal, use the Pulse Wave option of the Generator. Set Width Units to Samples, then set Pulse A Width to 1024 samples, and Pulse B Width to 0. Make sure Pulse A Level is 100%.

Make sure Trigger is active and set to Gen Sync mode, and set the Trigger Delay to zero. While viewing the unexpanded waveform of the output channel, you should see a flat line at the top of the trace. Set the pulse frequency low enough that the pulse will be off for at least as long as it's on, which at a sample rate of 44100 Hz will be 22 Hz or less.

Here's one difference with the Impulse response method: You can't see a valid response by looking at the output channel directly in Spectrum mode. All you will see is a full-scale value at DC, and zero values everywhere else. That's because as far as the FFT responsible for the spectrum is concerned, you only have a DC signal; it only looks at 1024 samples, and all those are at full-scale.

Now, with Spectrum off, connect the output channel back to the Input. You should see a big spike at the start of the trace that decays toward zero. Toggle Spectrum on and you will see a spectrum that also decays toward zero. Make sure Y-log is active, and hit the Curves button to pop up the Spectrum Curves dialog. Toggle on the +6 dB/Octave Tilt for the selected Input channel, and the falling part of the trace will be boosted toward the DC value. You should see a reasonably flat trace, though typically with noise and irregularities at the high frequencies.

Important: Never use a Window function when viewing the spectrum of a step response or any other transient event that is completely captured in the 1024 input samples used to create the spectrum. Window functions reduce the initial portion of the response, which will seriously compromise the spectrum of the transient. Use Window functions only for continuous waveforms.

Note that the output stimulus signal is not really a step, due to the fact that the sound card output is AC coupled to block DC. And, even if you produce a true step in some other way (perhaps via a lab-type test oscillator generating a square wave), the sound card input is also AC coupled so the response won't look like a step. The speaker itself won't be able to create a true step output unless it is driving a sealed chamber and the speaker mechanism (cone, dome, and surround) has no air leaks. But as long as the frequency response of the sound card goes substantially lower than the response of the speaker, there should be no problem. That should be the case with most sound cards, which have responses down to a few Hz.

One problem with the Step response method is that the +6 dB per octave Tilt tends to disproportionally boost the high frequency noise that is naturally present. This may obscure the true response at high frequencies. Synchronous waveform averaging will help to reduce this problem.

The Step response is typically about 45 dB stronger than the Impulse response on the same system, so less averaging (if any) may be needed to resolve the low-frequency portion of the response. However, since the Tilt is boosting the high frequency noise, there is progressively less advantage at higher frequencies. You will need to judge the utility of this method for your particular situation.

Instead of a true 0-100% step you can use a Square wave that runs between +/-100% of full scale. This is slightly easier to set up since you just set Square with a frequency of 22 Hz or less; no fiddling with Pulse widths. Best of all, the response is boosted by 6 dB since the signal has twice the effective amplitude. Otherwise, everything else is the same.

See also Frequency Response Measurement

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