Applied Problem Solving: Speech Signal Analysis Consider the design of a system to recognize the spoken words for the ten digits: “zero,” “one,” “two,” . . ., “nine.” A first step in the design is to analyze data sequences collected with a microphone to see if there are some statistical measurements that would allow recognition of the digits. The statistical measurements should include the mean, variance, average magnitude, average power and number of zero crossings. If the data sequence is x(n), n = 1, . . . , N , these measurements are defined as follows: 1 N N mean = µ = x(n) n=1 1. | Applied Problem Solving Speech Signal Analysis Consider the design of a system to recognize the spoken words for the ten digits zero one two . nine. A first step in the design is to analyze data sequences collected with a microphone to see if there are some statistical measurements that would allow recognition of the digits. The statistical measurements should include the mean variance average magnitude average power and number of zero crossings. If the data sequence is x n n 1 . N these measurements are defined as follows mean ụ N x n n 1 1 standard deviation Ơ 1 N 1 2 N x n - ụ 2 n 1 average magnitude N x n n 1 1 average power N N x n 2 n 1 The number of zero crossings is the number of times that x k and x k 1 differ in sign or the number of times that x k x k 1 0. Matlab functions for reading and writing Microsoft wave .wav sound files include Function Description x wavread wavefile Reads a wave sound file specified by the string wavefile returning the sampled data in x. The .wav extension is appended if no extension is given. Amplitude values are in the range -1 1 . x fs bits wavread wavefile Returns the sample rate fs in Hertz and the number of bits per sample bits used to encode the data in the file. wavwrite x wavefile Writes a wave sound file specified by the string wavfile. The data should be arranged with one channel per column. Amplitude values outside the range -1 1 are clipped prior to writing. wavwrite x fs wavefile Specifies the sample rate fs of the data in Hertz. The following is a script to prompt the user to specify the name of a wave file to be read and then to compute and display the statistics and to plot the sound sequence and a histogram of the sequence. To compute the number of zero crossings a vector prod is generated whose first 175 element is x 1 x 2 whose second element is x 2 x 3 and so on with the last value equal to the product of the next-to-the-last element and the last element. The find function is used to determine .
