Zachary asked . 2021-01-11

Why do I observe a shift in mean when using the DECIMATE function in MATLAB 6.5 (R13)?

When I use the DECIMATE function using the following command:

load p3.txt

plot(p3(:,1),p3(:,2),'k.');

grid on; hold on;

y=decimate(p3(:,2),31);

y2=decimate(p3(:,2),31,n);

t=linspace(p3(1,1),p3(end,1),255)';

p3dec31=[t y];

plot(p3dec31(:,1),p3dec31(:,2),'g*',t,y2,'go');

[mean(p3(:,2)) mean(y)]

I observe a shift in the mean when viewing the plot. I can also verify the same from the command line:

[mean(p3(:,2)) mean(y)]

 as these two values are different.

matlab , functions

Expert Answer

Prashant Kumar answered . 2024-12-21 16:16:58

The shift in the mean is caused by the order of the filter used in DECIMATE. By default, an 8th order Chebyshev Type I Low Pass Filter is used as an anti-aliasing filter before removing samples. However, there is a cost function that evaluates the magnitude response of the filter at the cut-off frequency to determine the filter order. Depending on the machine used (Intel Pentium, AMD Athlon, etc) and the operating system (Windows XP, Linux, etc), different numerical libraries produce different results in the cost function and as a result, different filter orders are selected for the same DECIMATE command.

Even order filters generate a 0.05 dB attenuation at f = 0, which then produces the shift in the mean. Odd order filters do not exhibit this behavior at f = 0 and hence do not produce the shift in the mean.

The workaround is to use DECIMATE with the FIR filter option. The FIR filter does not have a 0.05 dB attenuation at f = 0 and hence the shift in mean does not appear in the downsampled signal.

The reason for evaluating the cost function that computes the magnitude response of the filter at the cut-off frequency is that as the passband-edge frequency decreases, the filter that is designed may degenerate for the default 8th order filter. You can see the distortion by following these steps:

1. Start MATLAB

2. Open decimate.m

3. Put a breakpoint on line 126 of decimate.m

4. In the Command Window, enter the following command:

decimate([1:10],61)

5. When MATLAB breaks at line 126, view the 8th order Chebyshev Type I IIR filter by entering the following command:

fvtool(b,a)

6. Zoom into the cut-off frequency of the filter and you will notice that the passband has significant distortion.

The distortion is caused by forming the transfer function from poles and zeros and the roundoff error that accumulates from the convolutions involved. By lowering the filter order, we can reduce this distortion significantly. You can verify this by resuming the MATLAB debugger and viewing the frequency response of the 7th, 6th, etc order filters at the cutoff frequency.

Not satisfied with the answer ?? ASK NOW

Recent Matlab Projects

Classification of Covid and Non-Covid Lungs CT-Scan using Deep Learning with MATLAB

Matlab simulation on Wind Energy system

Frequently Asked Questions

MATLAB offers tools for real-time AI applications, including Simulink for modeling and simulation. It can be used for developing algorithms and control systems for autonomous vehicles, robots, and other real-time AI systems.

MATLAB Online™ provides access to MATLAB® from your web browser. With MATLAB Online, your files are stored on MATLAB Drive™ and are available wherever you go. MATLAB Drive Connector synchronizes your files between your computers and MATLAB Online, providing offline access and eliminating the need to manually upload or download files. You can also run your files from the convenience of your smartphone or tablet by connecting to MathWorks® Cloud through the MATLAB Mobile™ app.

Yes, MATLAB provides tools and frameworks for deep learning, including the Deep Learning Toolbox. You can use MATLAB for tasks like building and training neural networks, image classification, and natural language processing.

MATLAB and Python are both popular choices for AI development. MATLAB is known for its ease of use in mathematical computations and its extensive toolbox for AI and machine learning. Python, on the other hand, has a vast ecosystem of libraries like TensorFlow and PyTorch. The choice depends on your preferences and project requirements.

You can find support, discussion forums, and a community of MATLAB users on the MATLAB website, Matlansolutions forums, and other AI-related online communities. Remember that MATLAB's capabilities in AI and machine learning continue to evolve, so staying updated with the latest features and resources is essential for effective AI development using MATLAB.

Without any hesitation the answer to this question is NO. The service we offer is 100% legal, legitimate and won't make you a cheater. Read and discover exactly what an essay writing service is and how when used correctly, is a valuable teaching aid and no more akin to cheating than a tutor's 'model essay' or the many published essay guides available from your local book shop. You should use the work as a reference and should not hand over the exact copy of it.

Matlabsolutions.com provides guaranteed satisfaction with a commitment to complete the work within time. Combined with our meticulous work ethics and extensive domain experience, We are the ideal partner for all your homework/assignment needs. We pledge to provide 24*7 support to dissolve all your academic doubts. We are composed of 300+ esteemed Matlab and other experts who have been empanelled after extensive research and quality check.

Matlabsolutions.com provides undivided attention to each Matlab assignment order with a methodical approach to solution. Our network span is not restricted to US, UK and Australia rather extends to countries like Singapore, Canada and UAE. Our Matlab assignment help services include Image Processing Assignments, Electrical Engineering Assignments, Matlab homework help, Matlab Research Paper help, Matlab Simulink help. Get your work done at the best price in industry.