I needed a sound sleepto calmmy mind. Here the underlined part is a/an -

• I needed a sound sleep to calm my mind. Here the underlined part is a/an - Non-finite verb.
• A non-finite verb is a verb form that does not show tense.
- Most non-finite verbs found in English are infinitives, participles and gerunds.
- প্রশ্নে উল্লেখিত বাক্যে to calm হচ্ছে infinitives এবং এই verb দ্বারা কোনো tense নির্দেশ করছে না। 
- তাই এটি non-finite verb.