# Calculating THD vs. Frequency of an Acoustic System using the Exponential Swept Sine Method

I am working on analyzing the total harmonic distortion (THD) vs. frequency curve for an acoustic system. I am aware of the traditional method of exciting the system with a mono-frequency wave and measuring the fundamental and harmonic frequencies, but it is too time-consuming for my requirements.

Instead, I am considering using the exponential swept sine (ESS) method to continuously excite a range of frequencies and then applying deconvolution techniques using the time-reversed and amplitude-modulated signal of the ESS. This approach allows me to obtain the impulse response of the linear part and the harmonic distortion part separately in the causal and anti-causal parts of the deconvolution result.

Now, I would like to calculate the THD against frequency based on these results. Initially, I attempted to use the Fast Fourier Transform (FFT) of the impulse response of the fundamental and each order of harmonics. However, I found that the calculated THD using this method differs from the THD obtained via the mono-frequency measurement.

In addition, I have encountered a potential issue with this method related to the power of each frequency component not being constant. I would like to measure the THD under a specific power level, such as 10W, but I'm unsure how to proceed. Given that the ESS method excites a range of frequencies continuously, the power of each frequency component may vary throughout the sweep. This variation in power makes it difficult to accurately measure the THD at a specific power level.

Could someone please guide me on how to correctly calculate the THD vs. frequency using the deconvolution results from the ESS method? Is there a specific approach or formula that I should follow to obtain accurate THD values? I appreciate any insights or alternative methods that could help me achieve my goal efficiently. Thank you in advance!

• Just added a link to an answer elsewhere here on SE.SP that explains one way of doing ESS.
– Peter K.
Jun 7 at 12:19
• Hi DSP Novice, it's all in the data, the distortion I mean. You have the measurements that if shared with readers then some one would reproduce the explanation in the question and better assist. Any chance to have the input output signals of your THD measurments. It hasn't got to be the entire measurment if the files are large, but a sample would be required. Jun 12 at 22:08