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Recent innovations in wearable biomedical sensors have provided new opportunities for development of tele-diagnosis applications. This paper describes a new technique for preliminary detection of cardiac arrhythmias during remote monitoring of Holter ECG signals. This research utilizes sufficient statistics of maxima of ECG signal's aggregate spectrum for initial diagnostics. Aggregate spectrogram (AS) has been computed for fixed length, sliding but disjoint windows. Maxima of AS are continuously sent to a remotely located clinical alarm station or diagnosis center where the trend is monitored for preliminary decision making. Sufficient statistics are computed from the maxima of AS at the diagnosis center. To make decisions, a linear classifier has been developed that uses sufficient statistics to differentiate between a normal and a diseased cardiac function. The classifier has been trained and evaluated using 63 different subjects from MIT Arrhythmia and Normal Sinus Rhythm Database. The proposed technique reduces transmission bandwidth and costs, prevents network congestion and is more helpful in getting instant pathological evidence rather than transmitting and analyzing the entire Holter ECG. Transmission bandwidth reduces by 1/fs L where fs and L are sampling rate and window length, respectively. The proposed method has linear complexity order. The sensitivity and specificity of the method come out to be 100% each, and it is especially effective in continuous ambulatory monitoring.