Integral transforms play an important role in many branches of science and en gineering. The history of integral transforms began with the mathematical tool known as Fourier transform, the oldest of all integral transforms, which has its limitation in applications. On the other hand, relatively a recent tool called Wavelets transform has an ability to decompose pertinent signal components, leading to several Wavelet-based techniques that supersede those based on tra ditional Fourier methods. The Wavelet transform gains great importance in the analysis of electrocardiograms by its suitability to process non-stationary signals. As a result, it is now accepted that the Wavelet analysis is far more superior in time-scale analysis of such signals. This study, based on discrete and continuous Wavelet transform implementation, investigates the extraction of constituent waves such as P wave, QRS complex, and T wave, besides the onset and offset of these waves in electrocardiogram signals with different mother wavelets in terms of their applicability. Detection of R-waves and estimation of R-peaks in electrocardiograms play a significant role in diagnosing heart rhythm irregularities and deciphering the heart rate vari ability. The parameters used to analyze the efficacy and accuracy of detection of R-peaks based on the Haar wavelet has achieved better sensitivity, positive predictivity, and detection error compared to some of the existing results in the literature. Also, it ascertains that the mother wavelet with small order works more efficiently than higher-order in the same wavelet family for the detection of R-peaks. Further, the introduction of five new mother wavelets viz three new real wavelets and two complex wavelets to carry out such analyses. The performance of these wavelets is compared with the well-known family of mother wavelets such as Morlet, Mexican hat etc. The accuracy and reliability of detection of R-peaks based on one of the proposed wavelet yields better sensitivity, positive predictivity, and detection error compared to those obtained based on well-known and other proposed wavelets. In addition, this approach is used to identify Myocardial Ischemia, which is a severe heart ailment. The data for this study is obtained from two publicly available sources such as MIT-BIH database and Apnea ECG Database.