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A SPEECH SIGNAL HAS A TOTAL DURATION OF 10SEC, IT IS SAMPLED AT A RATE OF 8KHZ AND THEN ENCODED. THE SNR IS REQUIRED TO BE 40DB. CALCULATE THE MINIMUM CAPACITY NEEDED TO ACCOMODATE THIS DIGITISED SPEECH SIGNAL.?
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A SPEECH SIGNAL HAS A TOTAL DURATION OF 10SEC, IT IS SAMPLED AT A RATE...
Introduction
To calculate the minimum capacity needed to accommodate a digitized speech signal, we need to consider several factors: the duration of the signal, the sampling rate, and the signal-to-noise ratio (SNR).
Given Parameters
- Duration of Speech Signal: 10 seconds
- Sampling Rate: 8 kHz (8000 samples/second)
- SNR: 40 dB
Calculating Total Samples
- Total samples = Duration * Sampling Rate
- Total samples = 10 seconds * 8000 samples/second = 80,000 samples
Bits Per Sample Calculation
Using the SNR to determine the bits per sample, we can use the formula:
SNR (in dB) = 10 * log10((2^n - 1)^2), where n is the number of bits per sample.
- Rearranging gives: n = log2(10^(SNR/10))
- For an SNR of 40 dB:
n ≈ log2(10^(40/10)) = log2(10^4) = 4 * log2(10) ≈ 4 * 3.32 ≈ 13.28 bits
- Rounding up: n = 14 bits per sample
Calculating Minimum Capacity
- Minimum capacity = Total Samples * Bits per Sample
- Minimum capacity = 80,000 samples * 14 bits/sample = 1,120,000 bits
Converting to Bytes
- Minimum capacity in bytes = 1,120,000 bits / 8 = 140,000 bytes
- Minimum capacity in kilobytes = 140,000 bytes / 1024 ≈ 136.72 KB
Conclusion
The minimum capacity needed to accommodate the digitized speech signal is approximately 140,000 bytes or 136.72 KB. This calculation ensures that the digitized signal meets the specified SNR of 40 dB for optimal quality.
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A SPEECH SIGNAL HAS A TOTAL DURATION OF 10SEC, IT IS SAMPLED AT A RATE OF 8KHZ AND THEN ENCODED. THE SNR IS REQUIRED TO BE 40DB. CALCULATE THE MINIMUM CAPACITY NEEDED TO ACCOMODATE THIS DIGITISED SPEECH SIGNAL.?
Question Description
A SPEECH SIGNAL HAS A TOTAL DURATION OF 10SEC, IT IS SAMPLED AT A RATE OF 8KHZ AND THEN ENCODED. THE SNR IS REQUIRED TO BE 40DB. CALCULATE THE MINIMUM CAPACITY NEEDED TO ACCOMODATE THIS DIGITISED SPEECH SIGNAL.? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A SPEECH SIGNAL HAS A TOTAL DURATION OF 10SEC, IT IS SAMPLED AT A RATE OF 8KHZ AND THEN ENCODED. THE SNR IS REQUIRED TO BE 40DB. CALCULATE THE MINIMUM CAPACITY NEEDED TO ACCOMODATE THIS DIGITISED SPEECH SIGNAL.? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A SPEECH SIGNAL HAS A TOTAL DURATION OF 10SEC, IT IS SAMPLED AT A RATE OF 8KHZ AND THEN ENCODED. THE SNR IS REQUIRED TO BE 40DB. CALCULATE THE MINIMUM CAPACITY NEEDED TO ACCOMODATE THIS DIGITISED SPEECH SIGNAL.?.
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