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Signal to noise ratio can be defined as the ratio of the level of the desired signal to the level of the background noise. It is given by SNR or S/N. SNR is expressed in Decibels(dB). When the SNR ratio is greater than 0 dB or higher than 1:1, it means that there is more signal than noise. SNR is widely used in the fields of engineering and mathematics to calculate the difference between the desired sound and background noise. The higher the value of SNR, the greater will be the quality of the received output. The formula for signal to noise ratio is,
SNR = \(\frac{\mu}{\sigma}\)
Where,
\(\mu\) is the mean
\(\sigma\) is the standard deviation
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Key Terms: Signal to Noise Ratio, Channel Capacity, Bandwidth, Noise, Speed, Signal, Frequency, Amplitude
Why is Signal to Noise Ratio Important?
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Signal to noise ratio plays an important role in communication systems. Sometimes, the signals in the transmission line get disturbed due to random noise in the background. For handling such situations, it is necessary to minimize the noise in the transmission process.
Also, Signal to Noise Ratio is important as it is used to calculate the strength of the signal. The exact signal and noise disturbance are calculated based on the SNR ratio
Read Also: Difference Between Echo and Reverberation
Signal to Noise Ratio
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SNR is the ratio of signal power to noise power and is given by:
SNR = \(\frac{P_{Signal}}{P_{Noise}}\)
Where,
P signal is the power of the signal
Pnoise is the background noise
Signal to Noise Ratio formula
SNR = \(\frac{\mu}{\sigma}\)
Where
\(\sigma\) is the standard deviation
\(\mu\) is the mean of the given data
Read More:
| Read More about Sound and its properties | ||
|---|---|---|
| Acoustics | Loudness of Sound | Reverberation |
| Sound Waves | Propagation of Sound | Reflection of Sound |
How to Calculate Signal to Noise Ratio
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The steps to calculate signal to noise ratio is,
Step 1: Calculate the mean(\(\mu\)) of the given data
Step 2: Calculate the standard deviation(\(\sigma\)) by substituting the values
Step 3: Substitute the values of mean and standard deviation in the Signal to Ratio formula.
Read Also: Coherent and Incoherent addition of waves
Channel Capacity
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Channel Capacity also known as Maximum Data Rate is what determines the speed of data transmission. The channel capacity is directly proportional to the power of the signal, as SNR = (Power of signal) / (power of noise).
It mainly depends on the following factors:
- The bandwidth available
- Number of levels in digital signal
- The quality of the channel
- The level of noise produced
Calculation of Channel Capacity and SNR:
Channel capacity is caluculated using the formula,
Capacity = bandwidth * log2(1 + SNR) bits/sec
Where
bandwidth is the bandwidth of the channel
SNR is the signal-to-noise ratio
capacity is the capacity of the channel in bits per second.
Read Also: Interference of light waves and young's experiment
Things to Remember
- The unit of Signal to Noise Ratio is (decibel) dB and not Hertz (Hz)
- Signal plays an important role in determining the quality of sound produced. If the signal is sufficiently strong, the audio signal-to-noise ratio is of high quality.
- The two main classifications for frequency-modulated signals are Frequency modulation Index and FM deviation ratio.
- Bandwidth is a fixed quantity, and cannot be changed. Thus, the channel capacity is directly proportional to the power of the signal, as SNR = (Power of signal) / (power of noise).
- The speed of sound depends mainly on the nature and the temperature of the medium through which it travels.
Read More:
| Read More topics from Sound Chapter | ||
|---|---|---|
| Characteristics of Sound | Reflection of Sound | Sonar |
| Structure of Human Ear | Oscillatory Motion | Frequency and Wavelength |
Sample Questions
Ques. Calculate the modulation index of an FM signal in which the modulation frequency is 2kHz and maximum deviation is 10kHz (3 marks)
Ans.
Given:
The maximum frequency of deviation: f\(\bigtriangleup \)max=10kHz
The maximum frequency of modulation: fm=2kHzfm
Substituting the given values in the above equation, we get:
m = \(\frac{f{\bigtriangleup}max}{f_m}\)
m = \(\frac{10}{2}\)= 5 khz
Hence, the modulation index of an FM signal in which the modulation frequency is 2kHz and maximum deviation is 10kHz is 5kHz
Ques. Compute the SNR of a 2.5 kHz sinusoid sampled at 48 kHz. Add white noise with a standard deviation of 0.001. Set the random number generator to the default settings for reproducible results. (3 marks)
Ans. 
Ques. A person is listening to a tone of 500 Hz sitting at a distance of 450 m from the source of the sound. What is the time interval between successive compressions from the source? (2 marks)
Ques. What is the range of frequencies associated with (a) Infrasound? (b) Ultrasound? (2 marks)
- Infrasound: Sound waves between the Frequencies 1 and 20 Hz.
- Ultrasound: Sound waves of frequencies above 20,000 Hz.
Ques. Flash and thunder are produced simultaneously. But thunder is heard a few seconds after the flash is seen, why? (2 marks)
As the speed of light is greater than that of the speed of sound, thunder is heard a few seconds after the flash is seen.
Ques. Calculate the overall noise figure for a three-stage cascade amplifier. When each stage has a gain of 12 DB and a noise figure of 8dB. (5 marks)
Ans. When the signal passes through various stages of an amplifier, the output has the original signal and some noise that gets amplified at different stages of amplifiers. Therefore, the final noise figure of the cascaded amplifier is obtained by,
We know,
F1 = 12, F2= 12, F3= 12
G1 = 8, G2 = 8, G3= 8
FN = 12 + (12- 1)/ 8+ (12- 1)/ 8 * 8
= 12 + 11/8 + 11/64
= 13.55
Therefore, the overall noise figure for a three-stage cascade amplifier is 13.55 dB
Ques. The frequency of a source sound is 100 Hz. How many times does it vibrate in a minute? (2 marks)
Ques. Distinguish between loudness and intensity of sound. (2 marks)
Intensity depends only on the energy per unit area of the wave and is independent of the response of the ear. Intensity is measured in Watt per meter square.
Ques. Explain the following: (3 marks)
a. Frequency
b. Time Period
c. Amplitude
Ans.
a. Frequency: The number of compressions or rarefactions are taken together passing through a point in one second is called frequency.
b. Time Period: Time Period is the time taken by two consecutive compressions or rarefactions to cross a point.
c. Amplitude: Amplitude is the magnitude of maximum displacement of a vibrating particle about its mean position.
Ques. Calculate the signal to noise ratio for the following data: 1,5,6,8,10 (5 marks)
Ans:
Mean of the given data:
\(\mu\)= \(\frac{1+5+6+8+10}{5}\)
The mean of the given data is 6.
Standard Deviation of the data given:
Now,
Signal to Noise Ratio = Mean/ Standard Deviation
=6/3.39
Therefore,
Signal to Noise Ratio =1.77 dB
Ques. A sound wave has a frequency of 2 kHz and wave length 35 cm. How long will it take to travel 1.5 km? (3 marks)
Ans.
Given,
Frequency, ν = 2 kHz = 2000 Hz
Wavelength, λ = 35 cm = 0.35 m
We know that speed, v of the wave = wavelength × frequency
v = λ ν
v = 0.35 m × 2000 Hz
v = 700 m/s
The time taken by the wave to travel a distance, d of 1.5 km is Thus sound will take 2.1 s to travel a distance of 1.5 km.
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