When analyzing for frequency content using the DFT (Discrete Fourier Transform), The frame which you are sampling is mathematically assumed to be periodic. Shown next is the exact same data shifted 1/2 of a period. Note that there is now a discontinuity in the waveform (which was at the edges in the previous picture).
For accurate analysis of frequencies, you don't want to have that discontinuity because it is only an artifact of the frame being non-periodic. So we want get rid of the discontinuity by scaling the signal by a window, such as the Blackman 3-term window shown below.
To window a signal, multiply the signal and the window sample by sample as shown in the next picture.
Now notice that the discontinuity is gone because there is a zero in the window at that point as shown in the next picture. The next picture also shows the index position of a frame which is traditionally put into the FFT (or DFT).
The next two plots show the frequency content of the originally sampled signal, first using now window (usually called a square window). The second plot below uses the Blackman window in the analysis of frequency magnitudes.
If you are asking the question What is the signal-to-noise ratio? for the D/A conversion of the voltages, you may answer 60 - 0 dB = 60 dB if you are looking at the square windowed signal. The Blackman windowed signal has a more accurate measure of the signal-to-noise ratio: 60 - (-25) = 85 dB. From this measurement, we can guess that the A/D converstion has an accuracy of 14 bits (which will nominally give a signal-to-noise radio (dynamic range) of 6 time 14 bits = 84 dB. The NIDAQ card has 12-bit digital output resolution.
Next is a zoom-in on the fundamental frequency magnitudes of the input signal. The Blackman curve is closer to being the true frequency content. For finding the major components in the spectrum, either plot will suffice, but to find less important peaks in the spectrum, you have to used a windowed input signal. For example, the square-windows curve has a very slow fall off from 5 - 10 Hz. In either case, however, you can tell that the fundamental frequency is around 5 Hz.
CS 377B: HCI Technology Stanford University, Fall98 |
EE/CompE 2961: HCI Design San José State University, Fall98 |
CS 436: HCI Technology Princeton University, Fall98 |