Summary of Signal Generation with MATLAB. Example of DTMF in telephony
### Summary This article explains generating arbitrary voltage signals from digital formats using a PC sound card and MATLAB. It details the signal chain: digital samples move via a memory buffer to a Digital-to-Analog Converter (DAC), followed by an amplification stage. The text highlights Shannon's theorem for sampling frequency and notes that audio card amplifiers typically limit bandwidth to 20Hz–20kHz, effectively capping usable signal generation below 10kHz due to distortion at high frequencies.
Parts used in the Signal Generation Project:
- Memory buffer
- Digital-to-analog converter (DAC)
- Amplification stage
- PC sound card
- Matlab software
- Computer (PC)
In mathematics a signal is a real function of a real variable f(t). In electronics it represents the evolution of a voltage (or a current) over the time and depends on the performances of the stage of the amplifier. Through a memory buffer, samples move to a digital-to-analog converter that produces a voltage signal, after an amplification stage that can limit the generation of the signal. A possible analysis consists of use Matlab with a PC sound card and an example of DTMF.
1. Introduction
Simplified diagram to generate an arbitrary signal v(t) from a digital format v(i) is shown in figure 1.
First of all, the information is available in digital format, inside a file in the vector numbers format (samples). Through a memory buffer, samples move to a digital-to-analog converter that produces a voltage signal to output to the external world, after an appropriate amplification stage. Shannon’s theorem states that the sampling frequency fs must satisfy the following relation: fs ≥ 2B, where B is the absolute band of the output signal. Even if the DAC can assure high sampling frequency, the absolute band of the signal that has to be generated depends on the performances of the output stage of the audio card. Because it’s designed for sound applications, it’s equipped with an amplifier with a 200Hz-20KHz bandwidth (in the ideal case). It must be also taken into account that the output signal will be distorted in amplitude and phase, more around the upper cutoff frequency. All that limits the generation of signals having with bandwidth lower than about 10KHz.
At this point, the most important issues are:
1- to generate a file with the signal in the digital format.
2- to setup a hw/sw sysytem able to perform the digital to analog conversion chain (DAC).
For More Details: Signal Generation with MATLAB. Example of DTMF in telephony
- What is the relationship between sampling frequency and signal bandwidth according to Shannon's theorem?
The sampling frequency fs must satisfy the relation fs ≥ 2B, where B is the absolute band of the output signal. - How does the output stage of an audio card affect signal generation?
The amplifier in the output stage has a bandwidth of 200Hz-20KHz and limits signal generation to about 10KHz due to amplitude and phase distortion near the upper cutoff. - Can a DAC assure high sampling frequency?
Yes, even if the DAC can assure high sampling frequency, the signal generation is limited by the performance of the output stage of the audio card. - Where do samples move before reaching the digital-to-analog converter?
Samples move through a memory buffer to the digital-to-analog converter. - What type of file format contains the information in digital format?
The information is available in a file in the vector numbers format containing samples. - Does the output signal experience distortion?
Yes, the output signal will be distorted in amplitude and phase, especially around the upper cutoff frequency. - What are the two most important issues mentioned for this system?
The first issue is to generate a file with the signal in digital format, and the second is to setup a hardware and software system able to perform the digital to analog conversion chain. - What is the ideal bandwidth range for the amplifier in a sound application audio card?
The amplifier is equipped with a 200Hz-20KHz bandwidth in the ideal case.
