Constant ( N) is an integer that assumes the value necessary to bring the term Nf s closest to the input signal frequency ( f in). Table 1 is a compilation of various sinusoidal input signal frequencies ( f in) sampled at a fixed rate of 1000 Hz and the resulting alias frequencies calculated using equation (1). Let's expand upon this equation with some examples. Equation (1) shows that alias frequency is a function of the absolute value of the difference between the input signal frequency and the closest integer multiple of the sample rate. We can predict an alias frequency if we know the frequencies of the input signal and the sample rate. Which are the real ones and which are the aliases? Just like trying to interpret the car's motion from the movie by watching only the wheels, it's impossible to know, and there's too much riding on your measurement to guess. All you have is a conglomeration of changing signal amplitudes versus time. You don't have the convenient frames of reference of the movie. If the sample rate of the data acquisition system is too slow relative to the frequency of the signal, your measurement literally falls apart. But what if you were viewing a movie of just the car's wheels? In this context, if asked to determine the speed and direction the car was moving you might reach an entirely different, erroneous, and embarrassing conclusion.Įxtending the above example, you can think of the camera as the data acquisition system, and the rotating wheels as the signal it's digitizing. You subconsciously filter this anomaly out of your interpretation of the image because from other frames of reference it's easy to determine that the car is moving forward at a high rate of speed. What you're seeing is an alias frequency caused by a mathematical collision between the fast rotational rate of the car's wheels and the much slower frame rate of the camera used to record the image. While watching a movie of a speeding car you look at the car's wheels and they seem to be rotating impossibly slow, or even rotating backwards. To explore what that means, let's go to the movies. For our purposes in data acquisition, we can more accurately define an alias as an assumed or additional frequency. Webster defines "alias" as an assumed or additional name. What's important is not just your frequency of interest, but all the frequencies contained in the signal you digitize and how they compare to the sample rate you've chosen. While it's true that the so-called Nyquist rate of two times the highest signal frequency component is the sample rate required to eliminate alias frequencies, the often overlooked qualifier to this rule is that the signal being digitized must be bandwidth limited at a value equal to half the Nyquist rate. Do we really have to get into the details? After all, everyone knows that you only need to sample at twice the frequency of your signal of interest to get good results, right? If you answered "right!" to that last statement, perhaps you should read on. What You Really Need to Know About Sample Rateīy and large discussions of sample rate are like watching paint dry.
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