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113D_1_EE113D_CR8_FFT

113D_1_EE113D_CR8_FFT - University of Hertfordshire...

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University of Hertfordshire STUDENT'S GUIDE THE FREQUENCY DOMAIN (\/ OBJECTIVES LECTURE 4 THE FREQUENCY DOMAIN This lecture should achieve the following: Introduce phasor representation of sinusoids Introduce Fourier Series and Transforms Introduce Discrete Fourier Transform (DF!) Consider operational complexity ofDFTs Deduce a Radix-2 FFT algorithm Consider some implementation issues of FFTs with DSPs LECTURE 4 4-1 167
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University of Hertfordshire STUDENT'S GUIDE THE FREQUENCY DOMAIN USE OF FREQUENCY DOMAIN Frequency Respons e ) IAl tL r r . IAI SIGNAL FREQUENC IES> r. WILL BE ATTENUATED AND DISTORTED __ IA N'S 'A' • •• • •• JOHN'S 'A' SPEECH ANALYSIS RECOGNITION IDENTIFICATION SPECTRUM ANALVZERS CONVERT A TIME DOMAIN SIGNAL INTO FREQUENCY DOMAIN Frequency Domain In our previous lectures, we have made quite extensive use of frequency domain information about signals. For example, when demonstrating the effect of filtering, we examined the frequency content of signals. Similarly, in deciding the quality of filter performance, we considered the frequency response of filters. In general, such frequency domain information is extremely important and useful in signal processing. Let us consider two more applications where frequency domain information is useful. When we want to transmit signals along a telecommunication channel, it would be useful if we knew the frequency respo nse of the channel. On this information, we can decide what group of frequencies can be sent through the channel without much distortion. . Although our transparency only shows the amplitude information versus frequency, phase information is also necessary to ensure that the signal will travel through the channel without degradation of signal quality. . Some companies have already implemented security systems that rely on spe aker verification. With speech analysis, sounds are analyzed in order to recognize a command. Analysis of the frequency content of each sound plays an important part in its identification. For example, the lower figure in our transparency shows the frequency cont ent of the letter "A" as spo ken by two diff erent people. We can use this information to make a judgment about the letter spoken, or decide by whom it was spoken. In both cases, the frequency content of the signal provides vital information. Television sets that accept voice commands now exist. However, these sets require softwar e which is speaker-independent in order to recognize a word no matter by whom it was spoken. Again , all of this complex analysis must be performed in the frequency domain. LECTURE 4 4-2 168
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Universityof Hertfordshire STUDENrs GUIDE T HE PHASO R MODEL THE FREQUENCY DOMAIN --- -~ --:. - --;- .. Re CO MPLEX PL ANE 1m 1m • I maginary Re . Re. 1 PHASO R - VE C TO R RO TAT ING Speed · co rad per . e c o nd A m pli tu de - A 2. PoluFonn 1. Rec tangular Form xltl- a + Jb where A.~ and +- rot - tan .t!.- a x(t) " A . I(eDt) where e j(eDt) " COS(eDt) + j s ln (eDt) ro - 2", 1t - 180 degrees Before we can describe the process of
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