Question

请问有人能帮忙解释一下下面这个题吗？用MATLAB做，如果可以请给我您的邮箱地址，谢谢！

1. Download the file “message.dat” at [4]. This file contains the waveform of a voice message embedded in a sinusoid with frequency of 400 Hz, and the sampling frequency is 22000 Hz. Construct a least squares filter to recover the speech using the following steps: (1)Try the following MATLAB code to observe the spectrum of message:

[freq_resp,freq_index]=freqz(message,1,50000,22000); plot(freq_index,abs(freq_resp))

You will see the magnitude plot of the Fourier transform for message versus frequency in Hz. Can you see the dominant frequency component of message? Write down the dominant frequency with the use of the command max. For more information, try help freqz and help max.
(2)Since the interference is a sinusoid, it should be of the form:

n(t) = Acos(wt +f)
where w =800p while the amplitude A and the phase f are unknown.After sampling, the discrete-time interference signal is:
n[k ] = Acos(wkTs +f)
where Ts =1/ 22000 . From trigonometric identities,n[k ]can be written as:
n[k ] =Acos(f)cos(wkTs ) -A sin(f)sin(wkTs )
=an'1 [k ] +bn'2 [k ]
where n'1 [k ] = cos(wkTs ) and n'2 [k ] = sin(wkTs ) are known which can be considered as reference sources for n[k] while a =Acos(f) and b=-A sin(f) can be considered as the unknown weights to be determined. The least squares estimates for a and b are obtained from:

(d) After obtaining aˆ and bˆ , write MATLAB code to construct the recovered speech according to
sˆ[k ] =r[k ] -aˆ n'1 [k ] -bˆ n'2 [k ] Determine the speech content.

Answer 1

1.在[4]下载message.dat数据文件。文件包含一个带有频率为400HZ的正弦噪音的声波，样本的频率为22000HZ。请按照如下的步骤创建
一个最小二乘的滤波器回复初始的声波。
（1）利用如下的matlab代码来观察文件的频谱：[freq_resp,freq_index]=freqz(message,1,50000,22000); plot(freq_index,abs(freq_resp))
（2）你会看到在频域下文件经过傅里叶变换后的最大值点。这时，你能看出来包含在文件中的主频率信息吗？请使用max函数记录下主频信息，
可以使用help来查询freqz与max来获得更多帮助信息。
2.因为干扰为正弦波，它应该具有如下形式：n(t) = Acos(wt +f) 其中w =800p 振幅A 相位f未知。取样后（这里不理解，我认为是一种离散化的数值表示），
离散时间的干扰信号是n[k ] = Acos(wkTs +f) 式中：Ts =1/ 22000 经过三角恒等变换 n[k ] =Acos(f)cos(wkTs ) -A sin(f)sin(wkTs )
=an'1 [k ] +bn'2 [k ] 其中n'1 [k ] = cos(wkTs ) and n'2 [k ] = sin(wkTs ) 可以被当做求解的原始已知信息，a =Acos(f) and b=-A sin(f)
是应该被考虑的未知权重项，利用最小二乘法对a，b进行估计：（这里是不少打字了）
（d）得到a，b后，编写matlab代码恢复原始文件依据sˆ[k ] =r[k ] -aˆ n'1 [k ] -bˆ n'2 [k ]表达式。

追问

您好，谢谢您的解答，第三小问确实少公式了，想请问一下第三和第四小题用MATLAB怎么解，方便的话能不能请您把您的邮箱地址发给我，我把题目发给您。谢谢~

追答

我也只是达到翻译的水准，做题方面我对信号处理不是很了解啊。。。