Teledyne LeCroy WaveExpert 100H Operators Manual - Manual (Page 207)

Wave Expert
WE-OM-E Rev A
205
Improving Dynamic Range
Enhanced resolution uses a low-pass filtering technique that can potentially provide for three
additional bits (18 dB) if the signal noise is uniformly distributed (white). Low-pass filtering should
be considered when high frequency components are irrelevant. A distinct advantage of this
technique is that it works for both repetitive and transient signals. The SNR increase is conditioned
by the cut-off frequency of the ERES low-pass filter and the noise shape (frequency distribution).
LeCroy digital oscilloscopes employ FIR digital filters so that a constant phase shift is maintained.
The phase information is therefore not distorted by the filtering action.
Record Length
Because of its versatility, FFT analysis has become a popular analysis tool. However, some care
must be taken with it. In most instances, incorrect positioning of the signal within the display grid will
significantly alter the spectrum. Effects such as leakage and aliasing that distort the spectrum must
be understood if meaningful conclusions are to be arrived at when using FFT.
An effective way to reduce these effects is to maximize the acquisition record length. Record length
directly conditions the effective sampling rate of the scope and therefore determines the frequency
resolution and span at which spectral analysis can be carried out.
FFT Algorithms
A summary of the algorithms used in the oscilloscope's FFT computation is given here in a few
steps:
1. The data are multiplied by the selected window function.
2. FFT is computed, using a fast implementation of the DFT (Discrete Fourier Transform):
where: x
k
is a complex array whose real part is the modified source time domain waveform,
and whose imaginary part is 0; X
n
is the resulting complex frequency-domain waveform;
; and N is the number of points in x
k
and X
n
.
The generalized FFT algorithm, as implemented here, works on N, which need not be a
power of 2.
3. The resulting complex vector X
n
is divided by the coherent gain of the window function, in
order to compensate for the loss of the signal energy due to windowing. This compensation
provides accurate amplitude values for isolated spectrum peaks.
4. The real part of X
n
is symmetric around the Nyquist frequency, that is
R
n
= R
N-n
while the imaginary part is asymmetric, that is
I
n
= –I
N-n
The energy of the signal at a frequency n is distributed equally between the first and the
second halves of the spectrum; the energy at frequency 0 is completely contained in the