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A speech signal, band limited to 4 kHz, is sampled at 1.25 times the nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range – 5 V to + 5 V, are subsequently quantized in an 8-bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is _______ kHz.
Correct answer is '9.26'. Can you explain this answer?
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Most Upvoted Answer
A speech signal, band limited to 4 kHz, is sampled at 1.25 times the n...
Of -1 to 1, are quantized into 8 bits.
To determine the number of quantization levels, we need to consider the bit depth of the quantization. In this case, the speech samples are quantized into 8 bits, which means there are 2^8 = 256 quantization levels.
Now, let's determine the Nyquist rate. The Nyquist rate is defined as twice the highest frequency component in the signal. In this case, the speech signal is band-limited to 4 kHz, so the Nyquist rate is 2 * 4 kHz = 8 kHz.
The signal is sampled at 1.25 times the Nyquist rate, which is 1.25 * 8 kHz = 10 kHz. This means that 10,000 samples are taken per second.
Since the speech samples are uniformly distributed in the range of -1 to 1, and there are 256 quantization levels, we can calculate the quantization step size as the range divided by the number of quantization levels.
The range is 1 - (-1) = 2, and the quantization step size is 2 / 256 = 0.0078125.
Therefore, the quantization step size is 0.0078125.
To summarize:
- The number of quantization levels is 256.
- The Nyquist rate is 8 kHz.
- The signal is sampled at 10 kHz.
- The quantization step size is 0.0078125.
To determine the number of quantization levels, we need to consider the bit depth of the quantization. In this case, the speech samples are quantized into 8 bits, which means there are 2^8 = 256 quantization levels.
Now, let's determine the Nyquist rate. The Nyquist rate is defined as twice the highest frequency component in the signal. In this case, the speech signal is band-limited to 4 kHz, so the Nyquist rate is 2 * 4 kHz = 8 kHz.
The signal is sampled at 1.25 times the Nyquist rate, which is 1.25 * 8 kHz = 10 kHz. This means that 10,000 samples are taken per second.
Since the speech samples are uniformly distributed in the range of -1 to 1, and there are 256 quantization levels, we can calculate the quantization step size as the range divided by the number of quantization levels.
The range is 1 - (-1) = 2, and the quantization step size is 2 / 256 = 0.0078125.
Therefore, the quantization step size is 0.0078125.
To summarize:
- The number of quantization levels is 256.
- The Nyquist rate is 8 kHz.
- The signal is sampled at 10 kHz.
- The quantization step size is 0.0078125.
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Community Answer
A speech signal, band limited to 4 kHz, is sampled at 1.25 times the n...
Given
Speech signal/message signal frequency, fm = 4kHz
Sampling frequency, fs=1.25 fNR
Nyquist rate fNR=2fm=2*4= 8 kHz
Thus, sampling frequency, fs=1.25 fNR=1.25*8 kHz
Speech samples are uniformly distributed in the range −5V to 5 V and subsequently quantized in 8-bit uniform quantizer and transmitted over AWGN channel, so number of bits used by quantizer,
i.e., n = 8 Bit rate is given as, 8 10 8 kbps
Bit rate is given as, Rb= nfs=8*10=8kbps
According to channel capacity theorem,
Hence, minimum bandwidth required for reliable transmission is 9.259 kHz.
Question_Type: 4
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A speech signal, band limited to 4 kHz, is sampled at 1.25 times the nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range – 5 V to + 5 V, are subsequently quantized in an 8-bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is _______ kHz.Correct answer is '9.26'. Can you explain this answer?
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A speech signal, band limited to 4 kHz, is sampled at 1.25 times the nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range – 5 V to + 5 V, are subsequently quantized in an 8-bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is _______ kHz.Correct answer is '9.26'. Can you explain this answer? 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, band limited to 4 kHz, is sampled at 1.25 times the nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range – 5 V to + 5 V, are subsequently quantized in an 8-bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is _______ kHz.Correct answer is '9.26'. Can you explain this answer? 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, band limited to 4 kHz, is sampled at 1.25 times the nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range – 5 V to + 5 V, are subsequently quantized in an 8-bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is _______ kHz.Correct answer is '9.26'. Can you explain this answer?.
A speech signal, band limited to 4 kHz, is sampled at 1.25 times the nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range – 5 V to + 5 V, are subsequently quantized in an 8-bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is _______ kHz.Correct answer is '9.26'. Can you explain this answer? 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, band limited to 4 kHz, is sampled at 1.25 times the nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range – 5 V to + 5 V, are subsequently quantized in an 8-bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is _______ kHz.Correct answer is '9.26'. Can you explain this answer? 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, band limited to 4 kHz, is sampled at 1.25 times the nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range – 5 V to + 5 V, are subsequently quantized in an 8-bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is _______ kHz.Correct answer is '9.26'. Can you explain this answer?.
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