"Envelope methods" can be used to describe and predict the output characteristics of a highfrequency non-linear amplifier such as a travelling wave tube. Apparently one of these methods is known as IMAL.
There's several aspects to IMAL which I'd like to gain a better understanding of:
- I consider an input signal, which is a superposition of sine-waves of different amplitudes, phases and frequencies. I think I know how to compute the complex envelope of this signal. Both the amplitude and the time of the complex envelope, however, are time-varying. The nonlinear characteristics of the amplifier give the output amplitude and output phase according to the input amplitude. But using matlab, I clearly cannot assign to every of my time-varying amplitudes a new amplitude - it's just too many. I assume this is where linear interpolation is needed?
- Also apparently the signal is defined in frequency domain and then transformed to time domain. Why would I do that? I already know my signal is a superposition of sine-waves (which is time-domain, right?). I don't even know how to describe this signal in frequency domain.
IMAL is described in this article  as
Basically, IMAL utilizes an input signal defined in the frequency domain. An initial random phase value is assigned to each spectral line and the spectrum is converted into the time domain using the inverse fast Fourier transform (IFFT). As we are interested in the intermodulation falling in the amplifier band, the band-pass input signal is then converted to a complex lowpass equivalent one (complex envelope) and this is distorted using the nonlinear characteristics of the microwave amplifier. A linear interpolation routine is used to distort the signal and it is then transformed back to the frequency domain (FFT) to obtain the desired characteristics.
 "Computer Simulation of Intermodulation Distortion in Traveling Wave Tube Amplifiers" by Richard G. Carter, Wolfgang Bösch, Vishnu Srivastava, and Giuliano Gatti, in: IEEE Transactions on Electron Devices, Vol. 48, No. 1, January 2001. Available online from the University of Lancaster.