Hilbert Transform and Inverse Hilbert Transform (Definition, Formula, Basics and Properties of Hilbert Transform)

What is Hilbert Transform?

If x(t) is a signal and we represent its hilbert transform by xh(t), then xh(t) is obtained by providing '-π/2' phase shift to every frequency component present in x(t).

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Now let's see formula to calculate hilbert transform and inverse hilbert transform.

Hilbert Transform Formula

With the help of following formula we can easily calculate the hilbert transform

Inverse Hilbert Transform Formula

The formula provided here can be used to find the inverse hilbert transform

Now let's discuss properties of hilbert transform

Properties of Hilbert Transform

1. A signal x(t) and its hilbert transform xh(t) have the same energy density spectrum.

2. A signal x(t) and it's a hilbert transform xh(t) have the same autocorrelation function

3. A signal x(t) and its hilbert transform xh(t) are mutually orthogonal. We can write it mathematically as-

4. If xh(t) is a hilbert transform of x(t) then the hilbert transform of xh(t) is -x(t). 

It means -

if H[x(t)] = xh(t)

then H[xh(t)] = -x(t)

Here 'H' denotes the Hilbert transform.

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Ring Modulator - Construction and Working (Generation of DSB SC using Ring Modulator) - AM Generation

Here we will understand what is a Ring Modulator along with Where and Why the Ring Modulator is used? The structure and working of the ring modulator has been explained here with the help of beautiful circuit simulation software (Falstad Circuit Simulator). 

What is Ring Modulator (Ring Modulation)

A Ring modulator is an electronic device that is used for ring modulation.

Ring modulation is the implementation of frequency mixing. It is performed by multiplying two signals. One signal is a simple waveform (typically a sine wave) and another signal is the signal that we want to modulate.

Where and Why Ring Modulator is used

Ring modulator can be used to generate double sideband suppressed carrier (DSB SC) wave. DSB SC is a type of amplitude modulation where in the modulated wave contains only two side bands and the carrier wave is suppressed.

Why it is called Ring Modulator

The ring modulator circuit  implements diodes in clockwise or anticlockwise arrangement. Hence it takes the shape of a ring. That's why it is called as the ring modulator.

Ring Modulator Applications

A ring modulator finds applications in music synthesizer or as an effects unit.
The ring modulator heterodynes (frequency mix) two waveforms. The output is the sum and difference of the frequencies that are present in each waveform.

Ring Modulator | Construction and Working (Generation of DSB SC using Ring Modulator) | AM Generation Simulation 

Attributes: https://www.falstad.com/circuit/

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Amplitude Modulation Vs Frequency Modulation | AM Vs FM | Advantages and Disadvantages of AM and FM

What is Amplitude Modulation (AM)

Definition:-

Amplitude Modulation, is a system, where the maximum amplitude of the carrier wave varies, according to the instantaneous value (amplitude) of the modulating (message or baseband) signal.

What is Frequency Modulation (FM) 

In case of Frequency Modulation (FM) the frequency of the carrier wave varies according to the instantaneous value of the modulating (message) signal.

Comparison of AM and FM (AM vs FM)

Why FM is better than AM

Following reasons make the Frequency Modulation (FM) better than Amplitude Modulation (AM)

1.FM broadcasts operate in upper VHF (Very High Frequency) and UHF (Ultra High Frequency) ranges, while MF (Medium Frequency) and HF (High Frequency) ranges are used by AM broadcasts. This is a big advantage for FM, since in VHF and UHF frequency ranges there is less noise interference.

AM vs FM Video (Comparison of AM and FM) Video

 

2.FM receivers are more immune to noise in comparison to AM receivers. since FM receivers may be fitted with amplitude limiters. These amplitude limiters can remove the amplitude variations caused by the noise.

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#AMPLITUDE MODULATION (TIME DOMAIN EQUATIONS AND WAVEFORMS)

3.In FM, it is possible to further reduce noise by increasing frequency deviation. This is not possible in case of AM, since in AM, we can not exceed 100℅ modulation without Severe distortions.

4.Standard Frequency allocations provide a guard band between commercial FM stations. This leads to less interference between adjacent channels in FM in comparison to AM.

5.In case of FM, all the transmitted power is useful but in AM, most of the power is present in carrier, that does not contain any information.

AMPLITUDE MODULATION (TIME DOMAIN EQUATIONS AND WAVEFORMS)

What is Amplitude Modulation (AM)

Definition:-

Amplitude Modulation may be defined as a system, where the maximum amplitude of the carrier wave varies, according to the instantaneous value (amplitude) of the modulating (message or baseband) signal.

Note: [In case of Frequency modulation (FM), the frequency of the carrier wave varies, according to the instantaneous value of the modulating signal, while in Phase Modulation (PM), the phase of the carrier wave varies, according to the instantaneous value of the modulating signal.]

Amplitude Modulation (AM modulation) Video [HD]

 

What Will You Learn Here about Amplitude Modulation?

After reading this post, you will understand:-

#What is Amplitude Modulation (AM)

#Time Domain analysis of the Amplitude Modulation

#Equations of Amplitude Modulation (Time Domain)

#Waveforms of Modulating signal, Carrier signal and Amplitude Modulated wave and

#Properties of the amplitude modulation

Equations of Amplitude Modulation (Time Domain)

As per the definition of the amplitude modulation we can express it mathematically as-

FREQUENCY SPECTRUM OF AMPLITUDE MODULATION (WAVEFORMS AND EQUATIONS DERIVATION)

What is Amplitude Modulation (AM)

Definition:-

Amplitude Modulation, is a system, where the maximum amplitude of the carrier wave varies, according to the instantaneous value (amplitude) of the modulating (message or baseband) signal.

Note:- 

In case of Frequency Modulation (FM) or Phase Modulation (PM), the frequency or phase respectively, of the carrier wave varies, according to the instantaneous value of the modulating (message) signal.

FREQUENCY SPECTRUM OF AMPLITUDE MODULATION VIDEO [HD]

 

In the previous post, I discussed; what is amplitude modulation and its various properties. We talked about only the time domain analysis of the amplitude modulation. We saw here, how the waveform changes with time but here, we will discuss the frequency domain analysis of the amplitude modulation. Here you will see, how the spectrum of modulating signal, carrier signal and modulated wave looks like. I will also derive here the equation of AM wave in frequency domain. So let's start...