The EEG is a complex signal ensuing from postsynaptic potencies of cortical pyramidal cells and an of import encephalon province index with specific province dependent characteristics. Modern encephalon research is closely linked to the feasibleness to enter the EEG and to its quantitative analysis. EEG spectral analysis ( break uping an EEG signal into its constitutional frequence constituents ) is an of import method to look into the concealed belongingss and therefore the encephalon activities. Spectral analysis of sleep EEG signal provides acute penetration into the belongingss of different phases of slumber which can be utilized to place upsets. This paper describes the time-frequency analysis of human sleep Electroencephalogram signals through the usage of multi declaration Discrete Wavelet Transform and Fast Fourier Transform, which offers a representation of the signal in the time-frequency plane giving information sing the clip localisation of the spectral constituents at different phases of slumber in human existences. This paper besides discusses the some of the common pathological conditions associated with sleep EEG signals in brief.

The EEG ( Electroencephalogram ) signal indicates the electrical activity of the encephalon. The electrical activity of a encephalon ( EEG ) exhibits important complex behaviour with strong non-linear, random and non-stationary belongingss. The communicating in the encephalon cells take topographic point through electrical urges. It is measured by puting the electrodes on the scalp of the topic. The cortical nervus cell inhibitory and excitant postsynaptic potencies generate the EEG signals. These postsynaptic potencies summate in the cerebral mantle and widen to the scalp surface where they are recorded as EEG. A typical EEG signal, measured from the scalp, will hold amplitude of about 10 I?V to 100 I?V and a frequence approximately in the scope of 1 Hz to about 100 Hz. Electrode locations are specified by the 10-20 electrode arrangement system devised by International Federation of Societies for Electroencephalography. The 10-20 system is based on the relationship between the location of an electrode and the implicit in country of intellectual cerebral mantle. EEG, as a noninvasive testing method, plays a cardinal function in naming diseases and is utile for both physiological research and medical application. It helps in naming many neurological diseases, such as epilepsy, tumour, cerebrovascular lesions, depression and jobs associated with injury. EEG hints are different for different encephalon activities. The encephalon activity of an unnatural individual can easy be distinguished from a normal individual utilizing signal processing methods. There are assorted events, viz. : slumber, epilepsy, reflexology, drugs/anesthesia, diabetes, speculation, music and artifacts influence the EEG signal. However, it is really hard to acquire utile information from these signals straight in the clip sphere merely by detecting them. EEG signals are extremely non-Gaussian, non-stationary and have a non-linear nature. Hence, of import characteristics can be extracted for the diagnosing of different diseases utilizing advanced signal processing techniques. A figure of signal of signal processing techniques are available for the analysis of EEG signals ( like- Fast Fourier Transform, S Transform, Wavelet Transform etc. ) . The aim of this paper is to analyse characteristics of human sleep EEG signals utilizing Discrete Wavelet Transform and Fast Fourier Transform. These features of each of the sleep phases can play of import functions in naming sleep upsets.

Sleep Structure and States

Sleep EEG signals contain four spectral sets of clinical involvement. These are the I? set ( 1.3 -3.5 Hz ) , I? set ( 3.5 – 7.5 Hz ) , I± set ( 7.5 – 13 Hz ) and I? set ( 13 – 35 Hz ) . Sleep is by and large divided into two wide types: non rapid oculus motion ( NREM ) slumber and rapid oculus motion ( REM ) slumber. Based on EEG alterations, NREM is divided farther into four phases ( i.e. phase I, phase II, phase III, and phase IV ) . NREM and REM occur in jumping rhythms, the sequence being phase I, Stage II, phase III, phase IV, REM and begins once more with phase I. When encephalon is awake and busy, the encephalon moving ridges are desynchronized and really much guerrilla. When relaxed, encephalon generates moving ridges in I±- set. As the encephalon enters the sleep phases, the encephalon waves become increasingly slower and turn in amplitude. Fig.1 represents the sleep rhythms. The rhythm starts with phase I and ends with REM slumber. Each of the phases last around 12 – 15 proceedingss with the whole rhythm takes about 90-120 proceedingss. [ 1-2 ]

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Figure.1 The complete slumber rhythm

Phase I sleep

First indicant of phase I sleep is the slow peal oculus motions ( SREMs ) . Their distribution is rather similar to oculus motions in general ( considered as EEG Artifact ) . However, SERMs are slower ( i.e. typically 0.25-0.5 Hz ) . SREMs disappear in the consequent deeper slumber phases. By and large SERMs are accompanied by fading of the alpha beat ( alpha activity ) . The alpha activity bit by bit becomes slower, less outstanding, and fragmented. The other outstanding marks of phase I sleep are cardinal or frontocentral theta activity, enhanced beta activity, Positive occipital crisp transients of slumber ( POSTS ) , and Vertex crisp transients. POSTS amplitude varies in the scope of 50-100 AµV and they occur in 4-5 Hz scope. Vertex crisp transients ( 5 moving ridges ) like K composites of phase II slumber, vertex moving ridges are maximum at the vertex, normally appear symmetrically. Their amplitude is 50-150 AµV, can be contoured aggressively and happen in insistent tallies. They persist in phase II slumber but normally disappear in subsequent phases. Unlike K composites, vertex moving ridges are narrower and more focal. [ 1 ]

Stage II slumber

The distinguishable and outstanding characteristics of phase II slumber is the visual aspect of sleep spindles and K composites. The presence of sleep spindles is necessary and sufficient to specify phase II slumber. Sleep spindles have a frequence of 12-16 Hz ( typically 14 Hz ) and are maximum in the cardinal part ( vertex ) , although they are on occasion prevailing in the frontal parts. Amplitude is normally 20-100 AµV although utmost spindles can hold amplitudes every bit high as 100-400 AµV. K composites which are associated with the slumber spindles are besides an of import features of phase II slumber. K composites are high in amplitude ( & gt ; 100 AµV ) , wide ( & gt ; 200 MS ) , located in frontocentral part, with a typical upper limit at the midplane. Except for slow turn overing oculus motions, all characteristics of phase I sleep persist in phase II slumber. The outstanding forms of phase II slumber, spindles and K composites are normally easy to place and therefore are less prone to misunderstanding than the forms of phase I sleep.

Phase III and Stage IV Sleep

Phases III and IV sleep are normally known as “ slow moving ridge slumber ” or “ delta slumber. ” SWS or delta slumber is characterized by delta activity and comparative organic structure stationariness. Generally SWS is defined by the presence of such delta activity for more than 20 % of the clip with an amplitude degree of at least 75 AµV. the sum of delta activity separates phase III slumber from phase IV slumber. Phase III is defined by delta activity that occupies 20-50 % of the clip, whereas in phase IV, delta activity represents greater than 50 % of the clip. Sleep spindles and K composites may prevail in phase III and even to some grade in phase IV, but they are non outstanding.

REM slumber

REM slumber is characterized by rapid oculus motions, musculus atonicity, and EEG asynchronism ( compared to decelerate beckon slumber ) . In add-on REM slumber can besides be identified by the visual aspect of proverb tooth wave in the EEG recordings. The continuance of REM slumber additions increasingly with each rhythm and tends to rule tardily in the sleep period. The happening of REM excessively shortly after sleep oncoming, referred to as SOREMP, is considered pathological. [ 1-2 ]

Table I. summarizes the features of all the sleep phases with dominant spectral constituents, amplitude of the moving ridges and nature of the moving ridges.

Summary of all the sleep phases


Frequency ( Hz )


Waveform type

Wake up

15 – 50

& lt ; 50

Desynchronized Electroencephalogram


8 – 12


Alpha moving ridges

Phase I

4 – 8

50 – 100

Theta moving ridges

Phase II

4 – 15

50 – 150

Sleep spindles and K Complexes

Phase III

2 – 4

100 – 150

Sleep spindles and delta moving ridges

Phase IV

0.5 – 2

100 – 200

Delta moving ridges

Paradoxical sleep

15 – 30

& lt ; 50

Desynchronized EEG with low amplitudes and high frequences.

Multi-Resolution analysis and Wavelet transform

While analysing the EEG signals, it is non ever sufficient to hold the information about spectral constituent. Sometimes the clip localisation of these spectral constituents besides plays an of import portion in the analysis. Multi-resolution analysis provides the needed clip and frequence information by changing the declaration belongingss for different spectral constituents. Wavelet transform is a multi declaration analysis method. It possesses localisation characteristics both in clip and frequence sphere. Wavelet transform forms a general mathematical tool for signal processing with many applications in EEG information analysis as good. Its basic usage includes time-scale signal analysis, signal decomposition and signal compaction. [ 3-6 ]

Continuous Wavelet Transform

The Continuous Wavelet Transform ( CWT ) is described by the undermentioned equation,

Where ten ( T ) is the signal to be analyzed, I? ( T ) is the female parent ripple or the footing map, s is the scale parametric quantity and I„ is the interlingual rendition parametric quantity. All the ripple maps used in the transmutation are derived from the female parent ripple through interlingual rendition ( switching ) and scaling ( dilation or compaction ) . The interlingual rendition parametric quantity I„ relates to the location of the ripple map as it is shifted through the signal. Therefore, it corresponds to the clip information in the Wavelet Transform. The scale parametric quantity s is defined as |1/frequency| and corresponds to frequency information. Scaling either dilates ( expands ) or compresses a signal. Large graduated tables ( low frequences ) dilate the signal and supply planetary information about the signal, while little graduated tables ( high frequences ) compress the signal and supply elaborate information hidden in the signal. [ 3-6 ]

Discrete Wavelet transform

The Discrete Wavelet Transform ( DWT ) , which is based on sub-band cryptography, is found to give a fast calculation of ripple transform. It is easy to implement and reduces the calculation clip and resources required. The DWT of a sequence ten [ n ] is calculated by go throughing it through a series of half set high base on balls and low base on balls filters. The declaration of the signal, which is a step of the sum of item information in the signal, is determined by the filtering operations and the graduated table is determined by upsampling and downsampling operations. [ 3 ] First the samples are passed through a low base on balls filter with impulse response g [ n ] and a high base on balls filter with impulse response H [ n ] . The end product is the whirl of the two:

However, since half the frequences of the signal have now been removed, half the samples can be discarded harmonizing to Nyquist ‘s regulation. The filter end products are so downsampled by 2. The filter end products are so given by

Passing the input sequence through the half set filters one time form one degree of decomposition coefficients. Subsequent degrees of decomposition can be by cascading such filter Bankss with each degree of filter Bankss corresponds to that peculiar degree of decomposition. Fig.2 shows three degree DWT of the input signal which is denoted by the sequence x [ n ] , where N is an whole number. The low base on balls filter is denoted by g [ n ] while the high base on balls filter is denoted by H [ n ] . At each degree, the high base on balls filter produces detail information, while the low base on balls filter associated with scaling map produces harsh estimates.

Figure.2 Three degree DWT of the input signal ten [ n ]

DWT along with Fast Fourier Transform ( FFT ) can be a powerful tool for break uping and spectral analysis of biomedical signals ( like EEG signals ) .

Eeg Data and Practical Analysis

The sleep EEG recordings were obtained from Sleep EDF database under PhysioBank archives maintained by Massachusetts Institute of Technology ( MIT ) , which is a physiological signal archive for biomedical research. PhysioBank is a big and turning archive of well-characterized digital recordings of physiologic signals and related informations for usage by the biomedical research community. The EEG signals were obtained from 8 healthy topics both males and females aged between 21 – 35 old ages without any medicine contained FpzCz and PzOz EEG. The length of each information record is 1 hr, and each sampled at 100 Hz ( i.e. 360000samples ) . Practical analysis is composed of two chief

procedures: ( a ) filtering of EEG informations, and ( 2 ) decomposition of the filtered EEG signals.

EEG Data Filtering

The EEG informations were filtered utilizing 4th order set base on balls Elliptic filter. The base on balls set frequences were set from ( 2-to-40 ) Hz. The filtered signals have merely EEG moving ridges ( delta, theta, alpha, and beta ) with all the unsought frequence constituents removed, as the chief characteristic characteristics of different phases of the slumber lies in these low frequences.

Decomposition of Filtered EEG Data

The sleep phases revolve in rhythms and each of them lasts for around 12-15 proceedingss. The analysis at any clip within the period of each of the sleep phases in the rhythm should give the specific features associated with that peculiar slumber phase. In this paper, the sleep EEG signals were analyzed for each of the sleep phases with the aid of Discrete Wavelet Transform ( DWT ) and Fast Fourier Transform ( FFT ) . DWT is used to break up the EEG waves into elaborate coefficient and subsequently on the FFT is applied on the coefficients of each of decomposition degrees. The consequence of the FFT operation will uncover the major frequence constituents at each of the decomposition degrees. The features obtained from this analysis about conforms the coveted 1s.

Fig.3 is obtained by using FFT to the degree 4 and level 5 coefficients of the decomposition. From the FFT secret plan of degree 4 coefficients in Fig.3, it can be observed that the major frequence constituents are about 2.5 – 8 Hz, which accounts for the theta moving ridges. The spectral constituents around 0 – 0.5 Hz indicates the presence of slow turn overing oculus motions. The other noteworthy phenomenon is the deficiency of alpha activity denoted by the absence of spectral constituents around 9 – 12 Hz. These events are adequate to qualify phase I sleep.

Fig.4 is the FFT secret plan of the level4 and degree 5 coefficients of this signal between 25-30 proceedingss from the start of the EEG recording. It can be observed, that except the slow peal oculus motions, the other characteristics of phase I sleep are still predominating and the addition activity around 15 Hz histories for the sleep spindles.

Fig.5 represents the sleep EEG signal of the topic after 30 proceedingss of the start of the recording. The topic ‘s EEG signal is marked by slumber spindles which are the stigmata of phase II slumber. Fig.6 shows the K composites.

Fig.7 shows the frequence spectrum of the degree 4 and level 5 decomposition coefficients. The spectrum indicates the addition in delta activity which characterizes the phase III and phase IV slumber.

Figure.3 Frequency spectrum of degree 4 and level 5 decomposition coefficients within the clip runing from 5-15minutes from the start of the EEG recording.

Figure.5 Sleep spindles in EEG wave form.

Figure.4 Frequency spectrum of degree 4 and level 5 decomposition coefficients within the clip runing from 25-30minutes from the start of the EEG recording.

Figure.6 K-complex in Stage II EEG wave form

Figure.7 Frequency spectrum of degree 4 and level 5 decomposition coefficients within the clip runing from 45-55 proceedingss from the start of the EEG recording.

Clinical Correlation

The sleep EEG signals can be used to place upsets and abnormalcies. The healthy slumber EEG forms are matched with the forms under examination and can be analyzed for abnormalcies. Assorted sorts of neurological diseases can be identified with the aid of EEG signals. Sleep upsets, sleep apnea, mental hurt, epilepsy, tumours, cerebrovascular and other encephalon lesions etc. are a few outstanding names. Significant research activities are traveling around the universe to develop these techniques. With the betterment of the biomedical signal acquisition tools and signal processing techniques, it is likely that the effectivity and truth of this sort of analysis will turn up by manifolds.


Biomedical signal processing is one of the booming countries of modern scientific discipline and technology with EEG signal processing is one of the really of import aspects of this country. Enormous research and development activities are traveling around the universe. Medical scientific discipline in coaction with modern technology techniques can supply a monolithic sum of utile information and solutions in this field. Signal processing techniques are portion and package of EEG analysis. This paper used the technique of Discrete Wavelet Transform and Fast Fourier Transform to qualify the assorted phases associated with human slumber. This technique can be utile in pull outing characteristics of the biomedical signals. The truth of this technique is likely to be raised with the betterment of the biomedical signal acquisition tools, with the development of digital filters and of class with the development of more accurate signal processing algorithm.


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