we'll be dealing with 4 instruments today, 2 of them generate signals, and 2 of them display and analyse signals. RC audio generator(RC音频发生器) that will put out a variety of wave shapes. standard oscilloscope(标准示波器) to look at the signals in the time domain so we can see their shape spectrum analyzer(频谱分析仪) will analyze the signal into its Fourier components. basically the idea is to sample the incoming wave form convert that into digital form and then the spectrum in fact is computed digitally using a micro processor. So the overall system black diagram first consists of a system which is a low-pass filter and this low-pass filter is used in advance of the sampling process to basically reduce the artifacts that were introduce to the sampling. the input wave form comes in, it's filtered, sampled, and captured on a block basis putting to a digital memory and then a digital memory or micro processor computes the Fourier Transform and then that Fourier Transform is what we see on the display. So what we're computing of courese are samples of the Fourier Transforms. And so for example if the input let's say was a rectangular pulse, what would we in fact see on the display are samples of that as discrete frequencies or if as we have an input which is a square wave what will generate through the spectrum analyzer are the Fourier Series coefficient or equivalently the harmonic associated with the square wave. the square wave as we know is not harmonic function(非谐波函数), and so in fact the even harmonics are missing in teh square waves. This is fundmental, this is the third harmonic, fifth harmonic, etc. and then the amplitude of the square wave decays proportional to 1 over f which is the kind of analysis that we going through and look into Fourier Series. If we switch to the triangle wave, instead of their decaying as 1 over f, the harmonic's decay is 1 over f square as you see they drop off much more quickly. And again of course it's not a harmonic signal and so the even numbered harmonics are missing and maybe just, to kind of emphasize the point, we can show the sin wave again and the square wave again. The idea of injecting a carrier or not is related to the issue of whether or not we want to do synchronize or asynchronize demodulation(同步解调异步解调). The asynchronize demodulation correspongding to simply use of envelop detector