Huiswerkopgaven 5b - numerical problems
10 important questions on Huiswerkopgaven 5b - numerical problems
The American Standard Code for Information Interchange (ASCII) uses 128 distinct characters, each encoded in binary. A computer generates 120 000 characters per second
(a) How many bits are required to represent one ASCII character
The American Standard Code for Information Interchange (ASCII) uses 128 distinct characters, each encoded in binary. A computer generates 120 000 characters per second.
(b) What bit rate (bits/s) is needed to transmit the computer output? What is the minimum transmission bandwidth
(b) Bit rate: 120,000 × 7 = 840,000 bit/s = 840 kbps. By the Nyquist criterion the minimum bandwidth is BT = Rb/2 = 420 kHz.
The American Standard Code for Information Interchange (ASCII) uses 128 distinct characters, each encoded in binary. A computer generates 120 000 characters per second.
(a) n = log2 128 = 7 bits per character.
(b) Bit rate: 120,000 × 7 = 840,000 bit/s = 840 kbps. By the Nyquist criterion the minimum bandwidth is BT = Rb/2 = 420 kHz.
(c) A single parity bit is appended to each character for error detection. Recalculate
your answers to parts (a) and (b)
(c) With the parity bit, 8 bits per character. Bit rate: 120,000 × 8 = 960 kbps.
Minimum bandwidth: 480 kHz
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A telephone channel carries a voice signal band-limited to 4 kHz. The signal is encoded using PCM with a uniform quantizer.
(a) What is the minimum sampling rate
A telephone channel carries a voice signal band-limited to 4 kHz. The signal is encoded using PCM with a uniform quantizer.
(b) If 256 quantization levels are used, how many bits are required per sample
A telephone channel carries a voice signal band-limited to 4 kHz. The signal is encoded using PCM with a uniform quantizer(c) What is the resulting bit rate?
A telephone channel carries a voice signal band-limited to 4 kHz. The signal is encoded using PCM with a uniform quantizer
(d) What is the minimum channel bandwidth required to transmit this PCM signal
A telephone channel carries a voice signal band-limited to 4 kHz. The signal is encoded using PCM with a uniform quantizer
(e) If the quantizer uses 8-bit words but the channel bandwidth is limited to 32 kHz, what is the maximum number of voice channels that can be time-division multiplexed on this channel?
(e) Each PCM voice channel requires 64 kbps. A bandwidth of 32 kHz supports a maximum bit rate of 2 × 32,000 = 64 kbps (Nyquist). This exactly accommodates one channel – the channel is fully occupied by a single 64 kbps stream, leaving no capacity for additional channels. (In practice, oversampling margins and framing overhead would reduce this further
A compact disc (CD) records stereo audio, each channel band-limited to 20 kHz.
a) fs,min = 2 × 20 kHz = 40 kHz.
(b) n = log2 65536 = 16 bits per sample.
(c) Per channel: 44100 × 16 = 705.6 kbps. Both channels: 2 × 705.6 = 1.4112 Mbps.
(d) Minimum bandwidth: 1,411,200/2 = 705.6 kHz.
(e) For a sinusoid S = m2p/2. Using SNR = 3L2S/m2p with L = 216:
A 10-bit digital-to-analogue (D/A) converter has an output range of 0 V to 10 V.
(a) How many discrete output voltage levels does it produce?
(b) What is the voltage resolution (smallest voltage step)?
(c) A signal is reconstructed with a maximum voltage error of ±1/2 LSB. Express this error in millivolts.
(a) 2^10 = 1024 levels.
(b) Resolution = 10 V/(2^10−1) = 10/1023 ≈ 9.77 mV.
(c) 1/2 * LSB = 1/2 × 9.77 ≈ 4.89 mV
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