measure the bit rate

I load a data of ecg signal to matlab and manipulate it with lots of mathematics equations. At the end of the process I got a residual signal with low variance, that enable me compress the original signal. For example: I determine that every sample of the residual signal that has the value that is less than 0.05 equals to zero and I got a new residual signal that can be represented with half of the samples than before the zero reset. Now I do the mathematics manipulations backwards and get a new reconstructed ecg signal. My question is how can I measure the compression ratio? Can I measure the bit rate in the original signal and in the reconstructed one? If I can do it, what are the functions I need to use for calculating the bit rate of a signal that is represented by a row vector…?

Answer 1

[Walter Roberson]

Compression ratio is (total memory occupied by all variables needed to completely represent the compressed version of the signal) divided by (total memory occupied by all variables needed to represent the uncompressed version of the signal)

[maor]

Thanks for the quick answer. I referred to the answer in a new massage

Answer 2

[maor]

Yes that I already know. If I represent the reconstruct signal and the original signal by vectors of the same length, the total memory occupied by those vectors are the same (in case I export those vectors to txt file). Is there a way to measure the bit rate in matlab, because the reconstruct signal is represented by fewer bits per sample (due to the mathematics manipulation)..?

[Walter Roberson]

You said in your Question that the new residual signal can be represented in half of the samples that were required before the manipulation. Is it half the samples, or that fewer bits are used per sample ?

Answer 3

[maor]

somebody?? someone know the answer for that????

[Walter Roberson]

Yes, you can measure the bit rate and compare the two. However, the calculation involved will involve algebraic terms that "cancel" down to the same thing as taking the ratio of the size of the storage required.

[maor]

i didnt understand that. can you be more specific?

[Walter Roberson]

Bit rate for compressed data = number of bits occupied by compressed data, divided by time to send in.

Bit rate for uncompressed data = number of bits occupied by uncompressed data, divided by time to send in.

The ratio of the two = (#bits compressed / time) / (#bits uncompressed / time). The division by time cancel out, leaving (#bits compressed / #bits uncompressed)

And that is the formula I indicated above, ratio of the sizes. You can calculate the rate but the times cancel out algebraically leaving you with the sizes only, so you might as well just calculate those and ignore the rate.