# base - Charan Langton Editor SIGNAL PROCESSING SIMULATION...

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Charan Langton, Editor SIGNAL PROCESSING & SIMULATION NEWSLETTER Baseband, Passband Signals and Amplitude Modulation The most salient feature of information signals is that they are generally low frequency. Sometimes this is due to the nature of data itself such as human voice which has frequency components from 300 Hz to app. 20 Due to their low frequency content, the information signals have a spectrum such as that in the figure below. There are a lot of low frequency components and the one-sided spectrum is located near the zero frequency. Figure 1 - The spectrum of an information signal is usually limited to low frequencies . . . . . . . . . .

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The hypothetical signal above has four sinusoids, all of which are fairly close to zero. The frequency range of this signal extends from zero to a maximum frequency of f m . We say that this signal has a bandwidth of f m . In the time domain this 4 component signal may looks as shown in Figure 2. Figure 2 - Time domain low frequency information signal Now let’s modulate this signal, which means we are going to transfer it to a higher (usually much higher) frequency. Just as information signals are characterized by their low frequency, the transmission medium, or carriers are characterized by their high frequency. The simplest type of modulator for nearly all modulation schemes is called the Product Modulator consisting of a multiplier or a mixer and a band-pass filter. Let’s modulate the above signal using the Product Modulator, where m(t) is the low frequency message signal and c(t) is the high frequency carrier signal. The modulator takes these two signals and multiplies them.
Figure 3 - A Product Modulator The frequency domain representation of a Product Modulator or a mixer has a curious quality that instead of producing the products of the input frequencies which is what we really want, it produces sums and differences of the frequencies of the two input signals in both the positive and negative frequency domains. Is this a problem? The answer depends on what we want to do with the output. In most case if no non-linearity is present, we can predict exactly where these components will lie and we can filter out what we do not want. What if the carrier frequency source in a product modulator is not perfectly stable? In this case, each deviation frequency will also produce its own sum and difference frequencies with the baseband signal. These are called spurs and are inherent to the mixer process. In addition phase oscillations of the carrier also affect the output. For this reason simple mixer modulators and demodulators do not work well and further complexity in form of phase lock loops etc. is introduced into the receiver design. In Figure 4a, we see the two sided spectrum of the message signal. After mixing, modulating or heterodyning (all of these terms refer to the same thing), we get a spectrum such as in Figure 4b. The spectrum is now shifted up to the carrier frequency and we see that it is replicated on both sides of the y-axis.

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## This note was uploaded on 02/07/2011 for the course EE 567 taught by Professor Tutorials during the Spring '11 term at Birla Institute of Technology & Science, Pilani - Hyderabad.

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base - Charan Langton Editor SIGNAL PROCESSING SIMULATION...

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