| FrontPanel output sample Click on the left | Experiment with an Interactive Demonstration: Specify any Signal and Sampling Frequencies Below (see NOTE 2): To see the whole movie frame/graphics, set your display resolution to 1024X768 pixels and enlarge your browser to full screen. Type data for SIGNAL frequency and SAMPLING frequency in boxes below, and click Submit Query button below. |
NOTE 2: The above frequency values may be arbitrary. What is really important is the SAMPLING to SIGNAL frequency RATIO, not their absolute values (You may put SIGNAL freq. to 1 and any value for SAMPLING freq. will be the RATIO value also). If SIGNAL freq. is any integer multiple of SAMPLING freq., a zero (0) aliasing will result (You may put SAMPLING freq. to 1 and any integer value for SIGNAL freq. to verify this). Small ratio departure from zero aliasing will result in small aliasing frequency. The sampling at double signal frequency (SAMPLING/SIGNAL=200/100=2 ratio) is known as the critical value for aliasing, see NOTE 4 for definition of the Nyquist frequency. Around this value (i.g. RATIO=1.9 or 2.1 or similar), the so called "beat wave" interference occurs and it is interesting to try these. For a full "experience" it is the best to observe the results for the RATIO values from 0 to 2.2 in small steps and to 5 or 10 in larger steps. This could be done elegantly with actual continuous rotation of the RATIO knob on the virtual LabVIEW instrument, or putting it in the Auto RUN mode, see the Front-Panel (Sorry, cannot be done over the Internet yet!). For getting a realistic sampling of a SIGNAL, the SAMPLING frequency should be much more than double (Nyquist rule), more like 5 or 10 times the SIGNAL frequency. Actually, the RATIO value "physically" means the number of sampling points per cycle (or period) of the (real) SIGNAL, so the more the better.
NOTE 3: The PNG Query Form works faster with newer browsers (which support new PNG graphic format). With some (older) browsers there may be a "small" problem with the PNG graphics format. After submitting the Query, depending on the system setup, it may prompt to save resulting output file or to save it in TEMP directory without a prompt, but does not display it (does NOT support PNG - Portable Network Graphics format) in the browser. You may save the PNG file (about 25 KB, much smaller than the corresponding 125 KB JPG file) and display it in your application which supports PNG format (like Corel PHOTO-PAINT). You may have to change the file type to PNG in order to work. You may copy the corresponding URL address string in the Address-Bar, like:
http://http://www.kostic.niu.edu:88/cgi-bin/alias-cgi.vi?signl_f=100&sampl_f=190
The 100 and 190 values in the URL address string above are for the SIGNAL and SAMPLING frequency values, respectively. You may change/edit these values in the Address-Bar arbitrarily and REFRESH to get a new resulting screen in MS-IE.
NOTE 4: Nyquist frequency may be defined in different ways, namely: The above definitions represent the same phenomenon, i.e. the same critical frequency for aliasing, critical sampling twice the signal frequency, but are based on two different references: (1) the sampling frequency (so the Nyquist frequency is maximum signal frequency to be measured without aliasing, i.e. a half of the sampling frequency), and (2) based on a signal frequency (so the Nyquist frequency is the minimum sampling frequency required to avoid aliasing), thus the latter being twice the former.
