National Instruments 4551 User Manual page 61

Chapter 6 Advanced Concepts
NI-DSA Software User Manual
The power spectrum, normalized to 1 Hz bandwidth, gives the power
spectral density (PSD):
The use of the FFT for frequency analysis implies two important
relationships:
• The highest frequency that can be analyzed is related to the sampling
rate.
• The frequency resolution is linked to the total acquisition time, which
is related to the sampling rate and the block size of the FFT.
• Acquisition time = 1/f
of samples
To illustrate the above relationships, suppose that a digital time record,
obtained from discrete samples taken at a selected sampling rate, is used
to calculate a corresponding frequency spectrum composed of discrete
frequency samples, or bins. For real signals, the frequency spectrum has
half as many unique frequency bins as the time domain record has points.
If the FFT size used is 1,024, that is, 1,024 samples are acquired, and the
sampling rate is 204.8 kS/s, the complete time record acquisition will take
5 ms. This means that the lowest frequency in the spectrum corresponds to
the period of the time record itself:
The FFT of a 1024-point record has 475 alias-free lines, or 476 including
the DC bin. It does not have 512 lines because the width of the anti-alias
filter transition band is non-zero. To provide alias protection at the Nyquist
frequency (f /2), the filter also rejects some of the frequencies below the
s
Nyquist frequency.
475 lines 204,800 S/s
------------------------------------------------------- -
The spectrum obtained represents the frequency range from DC to 95 kHz
with 475 bins spaced every 200 Hz, as shown here:
lines
X k ( ) ⁄ (
2
PSD =
× N, where f
= sampling rate and N = number
s s
1
----------- = 200 Hz
5 ms
( )
1024 S
span 95 kHz
= ---------- - N = ------------------------ - 1024
F 204.8 kHz
S
6-4
)
Df
= 95 kHz
= 475
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