Question

With a diagram describe the Fourier representation of EMI.

Answer 1

Most signals generated by equipment and systems are quasi stationary: their parameters (amplitude, dominant frequencies, initial phases, damping coefficients, initial time instants etc.) are slowly time varying.The Fourier transform of the signal x(t) given by
F (x(t))-x(a) =亡x(t)e-iat dt
is local in frequency and global in time; because of this reason ܺ is suitable to characterize stationary signals in the frequency domain but is not capable of detecting transients and generally broadband impulsive noise in the time domain.

The practical implication of this consideration is that traditional frequency domain EMI receivers are not suitable to measure these types of signals because they assume stationary signals and therefore they refer to the conventional Fourier transform. In the past due to the presence of mainly analog communication equipment only continuous interference was considered harmful and therefore there was a limited interest in transient disturbances. In order to overcome this limitation in EMI receivers the usual approach is to sweep the frequency band of interest using a peak hold detector to record the maximum signal at each frequency. The major drawback of this approach is that the measurement time may be long and it is still not guaranteed the peak signal is measured. To perform radiated emission measurements from 30 MHz to 1000 MHz several hours are needed. Recent advances in high-speed sampling systems allow to use alternative test methods capable of overcoming this restriction. With the Short Time Fourier Transform, also known as the Gabor transform, implemented in time-domain EMI (TDEMI) test systems the measurement time has been reduced significantly. The Short Time Fourier Transform (STFT) can be used to determine local sections of a signal as it changes over time. The procedure to calculate the STFT is to divide a long time signal into shorter segments, where it is stationary, and then to compute the Fourier transform on each segment separately.

10 Spectrogram with Hanning window (200 samples) 80 90 100 110 120 130 140 150 10 Frequency (Hz) x 10 Spectrogram with Hanning window (100 samples) 100 110 120 130 140 150 10 Frequency (Hz) Fig.3 Spectrograms of the waveform of eq. (18): (a) Hanning window (200 samples), (b) Hanning window (100 samples)

Voltage waveform 0.2 0 0.2 0.4 0.6 -→ ャ | -1 0 500 1500 1000 Time(1/L microsecond) 2000 2500 5 Damped sinewave at the frequency of 256 MHz

The spectrograms are shown in above Fig using the Hanning window of length of 100 samples (a) and the rectangular window of length of 100 samples (b). Due to the small duration of the waveform, as shown in above Fig. the spectrograms occupy only the initial part of the time interval corresponding to about 0.5 microseconds; the frequency of 256 MHz is correctly identified.

Tim Time Frequency Time requency Time Computation of the STFT

In many TDEMI receivers after the data collection the STFT processing is implemented by using the Signal Processing Toolbox of Matlab because of its large library of available optimized functions.