Class 11 > Unit # 14: Communications > Digital Transmission of Speech or Music

Talha's Physics Academy

Analog-to-Digital (A/D) & Digital-to-Analog (D/A) Conversion Steps

Steps for Analog-to-Digital (A/D) Conversion

Natural signals like speech or music are acquired in analog form and converted into digital data using an Analog-to-Digital Converter (ADC). This translation involves three core steps:

1. Sampling

Sampling is the process of inspecting the instantaneous voltage value of an analog signal at regular time intervals. The time interval between successive samples is the sample period ($T$), and the number of samples taken per second is the sampling frequency ($f_s$).

To accurately reconstruct the analog signal at the receiver, sampling must be performed at or above the Nyquist rate ($f_N$):

$f_N = 2 f_{\text{MAX}}$

where $f_{\text{MAX}}$ is the maximum frequency component present in the analog signal.

2. Quantizing

Quantizing maps continuous sampled analog voltage values to a finite set of discrete voltage levels. An $N$-bit A/D converter utilizes $2^N$ quantization levels and divides the voltage range from $V_{\text{min}}$ to $V_{\text{max}}$ into intervals of size $q$ volts:

$q = \frac{V_{\text{max}} - V_{\text{min}}}{2^N}$

For example, a 3-bit ADC provides $2^3 = 8$ distinct quantization levels.

3. Encoding

In encoding, each quantized sample level is converted into an $N$-bit binary code word. For instance, a sample voltage of $0.613\text{ V}$ might be assigned the 3-bit binary value $110$.

The resulting digital bit stream is evaluated using the sample rate ($f_s$) and bits per sample ($N$) to calculate the bit rate ($R_b$):

$R_b = \text{sample rate} \times N = 2000 \text{ samples/sec} \times 3 \text{ bits/sample} = 6000 \text{ bits/sec}$

Fig: Step-by-step graphical representation of sampling, quantization, and encoding.

Digital-to-Analog (D/A) Conversion

At the receiving end of a digital communication system, the digital-to-analog converter (DAC) reconstructs the original information by converting incoming $N$-bit digital words back into corresponding discrete quantization voltage levels.

Each voltage level is held constant for one sample period, generating a characteristic stair-step signal. Although low-pass filtering can smooth out the staircase appearance, a slight discrepancy called quantization error remains between the reconstructed signal and the original analog waveform. Quantization error can be effectively minimized by increasing the number of bits ($N$) per sample, which decreases the size of the quantization intervals.

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