A 55-year-old man presents with a 2-month history of worsening exertional breathlessness and ankle swelling. He has a past medical history of hypertension treated with Ramipril 10mg OD. Examination reveals a displaced apex beat, bilateral pitting oedema to the mid-shin, and bibasal crackles on auscultation. An ECG shows sinus rhythm with left ventricular hypertrophy. What investigation is most crucial for diagnosing the underlying cause of his symptoms?